I am puzzled by the Russian phrase "я считаю, что," which is used very frequently. I know that an approximate translation is "I think that," but I strongly feel that there is some special idea, concept, or connotation behind the original phrase and that the translation "I think that" does not really grasp it.
I am especially interested to learn the difference between "я считаю, что" and "я думаю, что," since the latter phrase is the literal Russian translation of "I think that." I vaguely recall a teacher of mine explaining the difference between the following two phrases:
Я думаю, что он потратил много денег.
Я считаю, что он потратил много денег.
My recollection may be wrong, but is that the first sentence is a guess about how much money the person spent, and that the second sentence is rather a comment on an already known amount of spent money.
Wiktionary defines "считать" as "иметь мнение" ("to have an opinion"), but I am highly unsure whether this definition is precise. For instance, I remember the following phrase from a dialogue I had to learn:
Я считаю, что ты мне не подходишь.
In that dialogue this phrase is said by a girl to a guy, and the context is a date. At least in that dialogue, the sentence looked like a firm final decision rather than an opinion.
I am very curious how the native Russian speakers can explain "я считаю, что."
My question is this: What explanation of "я считаю, что" could you give to help me fully understand this phrase both consciously and on the emotional level?