Verb in volitional form (意向形)+と+思う is used to inform the interlocutor of the speaker's intention. 思う/思います is used to express this intention in the moment the speaker is speaking. 思っている/思っています is used to express that the decision of the speaker have been taken sometimes ago, but is still valid now. と思っている may be use to express the intention of a third person.
xephyer - thanks for your enthusiasm in adding stuff, but this is not grammar, this is vocabulary. please review the difference!
This entry should be deleted.
I intend to give a second life to this entry 平ら (たいら) [taira] changing it completely.