Vegtables have various classifications. One of them is based on the plant part we eat. So there are Fruit Vegetables ( Tomato, Eggplant etc), Leafy Vegetables ( Kales, Cabbage etc), Root Vegetables ( Radish, Carrot), Stem vegetables ( Kohl Rabi - also come under leafy), Stem tubers ( Potato), Inflorescence Veggies ( Asparagus). Hope that answers

Botanically, fruit refers to the structure of a flowering plant, ovary that encloses the seeds

Vegetables are the other plant parts except ovary, such as roots, leaves and stems

Actually, vegetables are a culinary category; they can include fruits as well as other plant parts. Fruit in the culinary sense (I shall separate this meaning of the word from the other by using the singular, not plural) is however largely restricted to fruits in the botanical sense. There would be differences between those fruits eaten as dessert fruit and those only eaten as vegetables, in terms of the compounds accumulated in them. Typically fruit is adapted for bird or mammalian dispersal, and as such it should contain a certain sugar concentration as reinforcing reward. Vegetables, even those represented by botanical fruits, may not meet this criterion. Another difference, though not a clear-cut one, is that fruit can be eaten raw, meaning it is unlikely to contain substances that need modification through cooking before ingestion. For this second difference, see our work attached.

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Fruit is a botanical term but not vegetable in strict term. However both are terms of economic botany. Tomato is vegetable in economic botany but it is a fruit. Apple is a fruit by botany and economic botany as well.

Taxonomic point of  view fruit is a ripened ovary of a flower.Vegetable is edible portion of a plant which does not include the ovary; of, or pertaining to the vegetative portion of the plant. Physiology point of view vegetable never come the stage of the repining stage before the repining stage mature stage harvested. In fruit, after repining condition harvested.Taxonomic description never use the vegetable as character but fruit is taxonomical important character. Vegetable generally use the world in the economic botany.   

Vegetables are popular names that can be  used for diferents parts of a plant, such as roots, fruits, leaves ( includind sheath) or stems. As Dr.  S. Proaches comments, "actually, vegetables are a culinary categor".

But, fruits are botanical term to designate  the ovary that was developt in Angiosperms.

There are two main types of fruit: fleshy or dry fruits, that can be Dehyscent ou Indehyscet

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Fruits and vegetables are commonly confused. The scientific (taxonomic) differences between them are clear. Scientifically speaking, a fruit is a matured ovary of a flower that has seeds. It has lots of taxonomical value. A vegetable, on the other hand, is any other edible part of a plant such a root, leaf or steam. From a culinary point of view, however, the differences between fruits and vegetables are much more complicated.

According to the Merriam-Webster Dictionary, a fruit is "the usually edible reproductive body of a seed plant; especially one having a sweet pulp associated with the seed." In other words, it is the edible part of a plant derived from a flower. Fruits are nature's instruments used to spread seeds. Thus fruits include apples, oranges, tomatoes, pumpkins, nuts, squash and pears.

Vegetables are herbaceous plant parts. They are the parts of the plant that are not fruits and can be used for eating. These parts include the root, leaf or stem of a plant. Some vegetables are radishes, carrots, broccoli, celery, garlic, onion, cabbage, potatoes, yams, lettuce and rhubarb

Fruits Thought to be Vegetables

Some fruits that are commonly thought to be vegetables are tomatoes, cucumbers, avocados, squashes, olives, peapods and peppers.

Technical vs Culinary Definitions

Despite the technical differences between fruits and vegetables, many fruits are treated as vegetables by cooks. Culinarily speaking, fruits are supposed to be sweet with seeds, and vegetables are any other plant products that are not sweet. Culinary vegetables include rhubarb, tomatoes, squash and peppers. Nuts, though technically fruits, are considered neither fruit nor vegetable in the culinary sense

Neither Fruit nor Vegetable

There are some plants that are neither fruit or vegetable. These include bananas, and mushrooms. Bananas, for example, are herbs. Mushrooms are fungi.

From a botanical point of view, fruit is a matured ovary that it has been pollinated previously, and overall it is characterizated by its sweetish, being generally perennial, for example orange, peach, pear, apple, apricot, plum, guava. Whereas vegetables is a term used for edible herbaceous parts of a plant cultured in a life annual cycle, such edible parts may be leaves (lettuce), roots (carrots), stems (celery), flowers (broccoli), fruits (tomatoes) so on. Likewise, another classification termed “horticultural products” not only includes vegetables but also other fresh products such as melon and watermelon.

Scientifically fruit is the matured, rather ripened seed bearing structure whereas vegetable is that plant part which is consumed as a supplementary plant product for the need of nutrition vitamins etc. Many fruits such as bringal and cucurbits are used as vegetables where as leaves (amaranthus), buds (Cabbage), flowers (Cauliflower) etc are  also consumed as vegetables.

Technically fruits are those nonpoisonous edible part which the plant give as a remuneration for the seed dispersal and may not always bee the ripened ovary as in the case of Apple where modified thalamus is the fruit and peduncle in Cashew.

Interestingly, in a philosophical thinking, vegetable is something man selected for his own convenience  whereas fruits are the gift of plants to all creatures  who help them in seed dispersal.