These are two commonly confused expressions here in Spain since both of them mean coger in some cases. Here are the differences between them:

1) Both could be used meaning coger in these examples:

I need to take/catch the 10 pm train to London.

There´s only a subtle difference between them: Catch involves a more passive character. You need to fit your schedule to be able to catch the bus. Take could probably involve more planning or control over the mode of transportation.

2) In other contexts, take means to get hold of something or gain possession of (take a pen and start writing), to transport or carry someone or something along (take the children to school, take that tube to the lab, etc.), and to do or perform an action (take a break/an exam).

There are many other definitions and uses of take but these are the ones which may be confused with catch.

Catch means capturing or seizing something ( throw the ball for the dog to catch it), to get hold of something especially forcibly or suddenly (he caught me by the arm), to take or get suddenly (caught a glimpse of the monarch).

In Spanish, we could probably translate take as tomar, coger, llevar, hacer  and catch as coger, atrapar or agarrar.

This is just a brief summary of the main differences between them but I recommend that you look both words up in a dictionary to get more information on their usage.

(sources: American Heritage Dictionary of the English Language, Fourth Edition and Collins Concise English Dictionary)