Crops such as carrots, beets, turnips and parsnips are all root true root crops consisting of a centralized tap root.

Potatoes, sweet potatoes and ginger are tuberous plants the tubers are actually underground modified stems.

Both are produced underground.

These attached photos should be useful for your understanding.

There are several categories to differentiate.. detailed illustration is given in these links:-

http://www.istrc.org/images/Documents/Symposiums/Fourth/4th_symposium_proceedings_7_02.pdf

https://www.hunker.com/13407021/the-difference-between-tubers-root-crops

https://en.wikipedia.org/wiki/Tuber

https://en.wikipedia.org/wiki/List_of_root_vegetables

https://www.hort.purdue.edu/newcrop/proceedings1990/v1-424.html

Aspidiotus is a genus of armored-scale insects that cause severe damage by piercing and sucking their host crops. They reproduce sexually by producing eggs that hatch into crawlers and crowlers that develop into sedentary adults. Their life cycles are typically around one month and their only mobile stage is the crawler stage. They prefer perennial than annual crops because perennial crops provide continuous source of food without a need for the crawlers to travel long distance once they have established. 

Root crops have modified roots to function as storage organs, while tuber crops have modified stems or roots to function as both storage and propagation organs. As such, the modified roots of root crops cannot propagate new crops, whereas the modified stem or roots of tuber crops can propagate new crops. Examples of root crops are potato, sweet potato, and dahlia; examples of tuber crops are carrot, sugar beet, and parsnip.

Well, root crops are crops where their taproot is modified into storage organ and then the toots are edible. Eg Carrots. In root crops you don't get any nodes and inter nodes. While tuber crops are crops which have underground modified stems and these modified stems act as main food storage organs are are edible. Eg Potatoes. In tuber crops the tubers have nodes where new shoots can be developed and can be used as a means of vegetative propagation. Similarities: both are geophytes, they anchor the plant, store food and water and

When looking at root and tuber crops compared to cereals the root and tuber crops can have high yields with more harvest efficiency. In a cereal crop a large mass of aerial support for the seed organs. In root crops their is greater shriveling of the plant and no need to have sturdy support stems. Another sizable advantage of roots and tubers that they are a fresher food having vital vitamins such as C which are scarce in dried grain. In some ways the soil offers a type of controlled storage. While the importance of cereals is widely recognized the value and worth of roots and tubers are less appreciated.

tuber are enlarged stem and root crops are enlarged tap root.furthermore, if any tuber cut many pieces it grow plant while in root crops cant grow plant.

Tuber crops include both tuberous roots and stem tubers, which act as storage organs. Crops with modified roots are distinct from those having modified stems. Such modified roots may be fleshy roots and tuberous roots, while modified stems may be tubers and corms. A fleshy root is an enlarged primary root as in carrot, ginseng (Panax spp.), and sugar beet, while a tuberous root is a thickened secondary root as in arrowroot, cassava, sweet potato, and yam bean. A tuber is an enlarged tip of an underground stem with leaves reduced to scales or scars subtending the auxillary buds, as in white potato and yam. Aerial tubers are called tubercle. A corm, as in elephant foot yam and tannia, is a short, solid, underground stem. To consider all the modified roots and underground stems, which store carbohydrates, we use the grouping “roots and tubers”.

I agree with previous answer!

A root is a compact, often enlarged storage organ with hairy stems that develops from root tissue. A tuber is also a root. More specifically, it's an enlarged storage organ, but it develops from elongated stem tissue, or rhizome. So a tuber is a root crop, but a plant can be a root and not a tuber.

Carrots and cassava are root vegetable crops. Potatoes, sweet potatoes and yams, on the other hand, are edible tuber crops. There are differences in the way edible root crops, or plants, grow and the way edible tubers grow.

Root and tuber crops consist of root crops, such as beets and carrots, and tuber crops, such as potatoes and sweet potatoes, and the leaves of root crops, such as beet tops.

Tuber is modified portion of underground stem /branch of plant where plant stored reserve food so it is underground swelling part of plant without containing root/ root hair. so it's function is only to store reserve food. It has some axillary buds looking as eye shape so when tuber is plated or tuber is cut into pieces this piece having eye is planted under favourable condition in the soil than it grow as new plant. i.e. vegetative propagation.

Where as in root crops, reserve food is stored in the main body of tap root so root is swelling and on the root body fibrous root system arriese so it absorb mineral nutrient and water from the soil and fix plant with soil.

The major difference between stem tuber and root tuber is the fact that stem tubers just like conventional stems have buds(eyes). Whereas, root tubers on the other hand do not bear buds(eyes) the same way conventional roots do not have buds.

Therefore, stem tubers can be cut and used in vegetative propagation while fragments of root tubers will not grow into new plants as they don't have buds.

Yam is a tuber crop while cassava is a root crop. One can be propagated, eg yam and cocoyam, while the other, cassava, cannot.

Stem tubers such as yam can be propagated from the storage organ (tuber) while root tubers such as cassava can be propagated from the stem.

Botanically speaking both rhizomes and tubers are modified underground stems.

In the case of the rhizome the extension with point upward and be able to sprout.

Tubers do not have the upward orientation but both are able to create a new plant being excellent for vegetative propagation by seed pieces as they are commonly called.