There are many different kinds of tests, so many in fact that companies often have a dedicated department, called quality assurance (QA), made up of individuals that spend their day testing the software the company developers produce.
To start making an initial classification, we can divide tests into two broad categories: white-box and black-box tests.
White-box tests are those which exercise the internals of the code, they inspect it down to a very fine level of granularity. On the other hand, black-box tests are those which consider the software under testing as if being within a box, the internals of which are ignored. Even the technology, or the language used inside the box is not important for black-box tests. What they do is to plug input to one end of the box and verify the output at the other end, and that's it.