The above video provides a quick look at different fruits and their botanical classification.

Flower

Plant reproductive organ that includes, among other features, an ovule-containing ovary.

For our purposes here a fruit is a product of a flower. Therefore, it is helpful to appreciate just what a flower is including, particularly, in terms of its component parts. Thus, from the outside going in, a complete (or so-called perfect) flower consists of sepals, petals, stamen, and carpels. The sepals are the bud coverings, the petals are the petals, the stamen is the male part or parts, and the carpels (a.k.a., pistils) is the female part or parts. A carpel in turn consists of what is known as the stigma, style, and ovary, and the ovary contains one or more ovules. The ovules becomes become the seeds and the ovaries usually will be what gives rise to the bulk of the fruit.

Fruit

Product of the post-fertilization maturation of a flower and representing a seed-disseminating plant organ.

Fruits are an integral part of the reproductive strategies of most flower-bearing plants. Indeed, fruits, strictly speaking, are produced only by flowering plants and develop in some capacity from the flowers of those plants. Their role in the flowering plant life cycle is to assure that progeny seeds are moved to some degree away from the parental plant so that they may invade new territories, more effectively compete against other plants, and in many cases not compete (or have to compete) against the parental plant. Also, fruits are not vegetables, though in fact a number of fruits nonetheless are often described as vegetables, such as squashes and tomatoes.

Types of Fruit	Simple, aggregate, and multiple as well as accessory, dry, or fleshy.
	There exists overlap between these different categories so a single fruit may be described by more than one of these descriptors.

Fleshy fruits

Achenes, berries, drupes, hesperidia, pepos, or pomes.

Fleshy fruits are fruits that are edible (or at least relatively easily masticated) when ripe and while still raw. In non-technical terms, fleshy fruits are typically equated with the concept of fruit. They can be contrasted with dry fruits which typically are not considered to be edible in their raw form. Note, though, that there are a number of fleshy fruits that nonetheless we may not necessarily think of as edible in their raw form, e.g., a squash, but nonetheless are in fact fleshy.

Dry fruits

Achenes, capsules, caryopses, legumes, nuts, and samaras.

Dry fruits are fruits that are less edible (or at not always easily masticated) when ripe and while still raw. In non-technical terms, fleshy fruits are typically not equated with the concept of fruit. They can be contrasted with fleshy fruits which typically are considered to be edible in their raw form. Note, though, that there are a number of dry fruits that nonetheless we may not necessarily think of as edible in their raw form, e.g., a sugar snap peas, but nonetheless are in fact dry fruits. In the latter case, though, it is an immature form that we consume and indeed a number of legumes (of which peas area a variety) are not normally consumed raw, or which in fact have their fruits discarded when we instead focus on consuming their seeds (e.g., various beans as well as peanuts). Alternatively, there are structures that we might imagine to be fruits, e.g., various tree nuts such as walnuts, which in fact are not fruits but instead which form within fruits (though normally we are not aware of these fruits when purchasing these products at the supermarket).

Simple fruit

Single, mature flower ovary that is normally found in isolation of other such mature ovaries.

A simple fruit not surprisingly is the simplest of fruits, derived from the simplest of flowers. Here a flower possesses only a single carpel/pistil and therefore only a single ovary. The flower furthermore is not closely associated on the plant with other, equivalent flowers. The ovary may or may not possess more than one ovule, but it matures otherwise in isolation from other carpels and thus forms a fruit that consists of the mature form of only a single ovary.

Aggregate fruit

Multiple, ovaries from a single flower that are found fused together in their mature form.

A flower that begins with multiple carpels/pistils and therefore multiple ovaries, all of which are found in isolation within the flower itself, will mature into an aggregate fruit. In other words, the resulting fruit will have been derived from multiple ovaries, but those ovaries will have all been found originally within a single flower. This contrasts with a simple fruit where the parent flower possessed only a single ovary. It also contrasts with multiple fruits where multiple ovaries instead are derived from multiple flowers.

Multiple fruit	Multiple ovaries from multiple flowers that are found fused together in their mature form.
	These multiple flowers that give rise to multiple fruits are found in close association and thus their fusion is not happen stance. Instead they can be viewed as literally multiple fruits that have fused into a single fruit, as though multiple apple flowers were so closely spaced that the resulting apples grew into each other. Indeed, the pineapple is one such multiple fruit.

Accessory fruit	Flowering plant seed-dissemination structure not derived from the plant's ovary.
	Apples, or pomes generally, are accessory fruits. Strawberries are accessory fruits with the ovary-derived achenes located outside of the accessory (here generally red) structure.

Achene	Dry fruit formed from a single carpel in which the seed and fruit are not fused.
	In many cases achenes are mistaken for seeds since the fruit is dry like a seed coat and indeed surrounds the seed. In some cases, particularly strawberries, achenes are associated with accessory fruit thus existing as both dry fruit (the actual mature ovary) and fleshy fruit (the accessory fruit). When achenes possess wings we call them samara.

Samara	Type of achene that possesses wings.
	These are dry fruits from which air foils form from the ovary wall. This allows increased potential for dissemination on the wind. Examples are the so-called "seeds" of the maples and the elms, which instead are actually fruit.

Berry	Fleshy fruits that mature from a single ovary.
	Berries are simple fruits and the most common type of fleshy fruits. As such, quite a number of fruits are berries, including many fruits that you would not imagine are berries. Thus, for example, tomatoes are berries though so too are grapes as well as peppers, bananas, and melons. Modified forms of berries include pepos and drupes.

Drupe	Fleshy fruit that surrounds what is known as a pit or stone that is derived from the ovary wall.
	Cherries and plums are drupes as so too peaches, olives, and even coconuts (though unlike these other examples, coconuts are dry rather than fleshy fruits). Blackberries and raspberries are examples of aggregate fruits that are aggregates of drupes (or drupelets). Mulberries are multiple fruits that are made up of multiple drupelets. Walnuts are the stones of a drupe.

Hesperidium	Fleshy fruits with leathery rinds.
	Hesperidia include the citrus fruits and all hesperidia are classified as modified berries. The segments of citrus fruits are called liths.

Pepo	Type of modified berry possessing a hard rind.
	Examples include though are not limited to squashes and cucumbers.

Capsule	Dry fruits that split apart or otherwise open when mature to release seeds.
	Horse chestnuts, Brazil nuts, and, I'm guessing, buckeyes are all examples of capsules as too are the fruits of cotton, willows, poppies, lilies, etc.

Caryopsis	Dry, simple fruit that is fused with the underlying seed coat and does not split open upon maturation.
	These fruits we describe as grains or cereals. That is, grains are not seeds (though contain seeds) but instead are fruits. That is, when we eat wheat or corn or rice, even refined wheat or corn or rice, we actually are eating fruits rather than simply seeds.

Legume	Pod-like dry fruits that develop from a single carpel and which possess a seam that separates the pod into two halves.
	Beans, peas, and peanuts are all legumes. Locust, mesquite, and Kentucky coffee trees are all legumes. Alfalfa is a legume as too also is clover. These fruits tend to be produced by plants that live in association with nitrifying bacteria and thus their seeds tend to be rich in protein and also they are able to enrich the environments in which they live with nitrogen.

Nut	Simple, dry fruit in which the seed-fused mature ovary is hard and woody.
	Nuts, in a botanical sense, should not be confused with the seeds of drupes (such as walnuts or almonds) nor with the seeds of capsule fruits (such as buckeyes or chestnuts). Acorns are examples of nuts and I believe as also are hazelnuts.

Pome	Fruit consisting of an ovary core that is surrounded accessory fruit.
	Apples are the most familiar of the pome fruits. Here the fleshy portion of the fruit is derived from the flower receptacle rather than the ovary whereas the seed-containing matured ovary is represented by the core. Some pomes, however, superficially resemble berries.

A few additional fruits: