What are the similarities and differences between grasshoppers and ants?

That is like asking "What are the similarities and differences between tigers and bats?" You cannot possibly have thought out what it was that you wanted to know. Grasshoppers differ in thousands of ways from each other and in even more thousands of ways from ants. They are both insects, but they are in different orders, just as tigers and bats are both mammals, but in different orders. They have the same number of legs and more or less the same type of blood and jaws, but they differ in size, in the food they eat, in the way they grow from the egg to the adult. (Grasshoppers come out of the egg looking like grasshoppers and they change their skins as they grow larger. Ant larvae are like grubs and they change into pupae and then into adult ants when they change their skins.) They differ in what they eat and how they collect their food. Ants are truly social insects. Grasshoppers are not (not even locusts are truly social).

Try asking yourself how you would like such a question answered before you ask. If you do so, then you are more likely to get an answer that you would like to read, one that would be useful to you. For instance, it might fit into less than a book. Do you just want to know how to tell whether an insect is a grasshopper, or an ant? (Like trying to tell whether a mammal is a tiger or a bat?) If you got this question from a teacher, ask the teacher how s/he would tell what the difference is between a tiger and a bat. Then criticise the answer because for every difference s/he mentions, there will be a hundred differences that s/he missed.