Hi Lindsey, penser means to think and croire means to believe. For the most part, they're pretty much interchangeable. (As much as they are in English.) Though, I would say penser is a little easier to use, since it's a regular verb, while croire can get pretty weird.
Hope that helps!
Being pedantic, there is a difference between think (penser) and believe (croire). I can think lots of things (six impossible things before breakfast), but do I believe them? A belief in my view is a more entrenched and permanent thought, so a pedant would take care which to use.
However, as Shelby says, in spoken English and French they are effectively interchangeable.
Effectivement ces deux verbes sont interchangeables.
Mais attention ; à la forme négative et à la forme interrogative, ils expriment le doute ; ils sont donc suivis du subjonctif.
Je pense/crois que tu as (ind.)compris.
Je ne pense pas que tu aies (sub.) compris. Je ne crois pas qu'il ait (sub.) compris.
Croyez-vous qu'elles aient (sub.) compris?