[KyleGoetz]

For the sense of taking something, 取る is just plain "take," while 受ける is "receive" and explicitly includes or implies that someone else was the "bestower." For example, 政府から弾圧を受ける is "be suppressed by the government," or, more literally, "receive suppression from the government."

Of course, 受ける has about a billion other meanings in addition to this one.

One of the only examples of 受ける literally meaning "to take" is when you "take a test." What's weird is テストを受ける is "to take a test," but paired with the intransitive equivalent 受かる, テストに受かる means "to pass a test."

In the case of a test, I think you can 取る it as well as 受ける. I can't think of any other examples off hand where they both mean "to take" and can be used interchangeably. I just vaguely recall saying 試験を取る my first year of Japanese, and then I learned 受ける and switched to 試験を受ける instead.