Instead of the leaves in a garden salad, vegetable salads are made with thinly sliced vegetables. There are two general types of vegetable salad; cold cooked vegetables and cold raw vegetables. Some vegetables need to be cooked to make them edible. Once they are cooked and cooled, they are treated as if they were raw vegetables.
Popular examples of raw vegetable salads include carrot and cabbage. The carrot salad is often made of finely grated carrot and has some pineapple and raisins as additions.
Cabbage is not as soft to eat as lettuce. However when cut up thinly it can be made into a salad. In addition to the salad dressing, common additions include carrot, apple, celery, onion, nuts etc.... Coleslaw is made of finely sliced cabbage, with a dressing. The word coleslaw comes from the Dutch, koolsla, meaning cabbage salad.
There are some popular salad vegetables that need cooking, these include potatoes and (especially dried) beans. A potato salad is made with small pieces of cold boiled potato in a salad dressing. They also often have additions such as cold boiled egg, sliced celery, lean meat and so on. While there are traditional recipes, a cook can make many choices within those traditions.
The potato comes from the South American country Peru. The first Europeans to discover the potato were the Spanish. The English word comes from the Spanish word, patata; but the word came into Spanish for a different vegetable.
Bean salads are made with cold cooked beans, that have been marinated in a dressing with a little onion. The word bean is Old English and has not changed for more than a thousand years; it must be an important word.
Many other cooked and cooled non-vegetable ingredients can make the salad more interesting. These include various cooked meats, but also seafood, pasta, cheeses, boiled eggs and so on. The nature of vegetables, such as potatoes, means that they have to be cooked to be edible, but once cooked and cooled are treated like vegetables that do not need cooking.
To summarise, a vegetable salad is
A cold mixture of thinly sliced vegetables covered with a dressing.
As with a garden salad, vegetable salads often will have additional foods to supplement the traditional recipe and a dressing is always required.