At first, there is no verb "möchten"!! "möchte" is Konjunktiv 2 of "mögen", it has no infinitive, because it is just a form, not a verb. So, wollen just means to want. I want coffee! Ich will Kaffee! I want to study. Ich will studieren. Ich möchte is more polite, as in english "i would like to" . I would like to have coffee. Ich möchte gern einen Kaffee. I would like to study. Ich möchte studieren. Now, if you use it with another verb, not a noun, it expresses more a wish than a real, important goal. If I say: Ich will studieren! It sounds like: I will!!! No mather what my parents say, I want it and i will! Ich möchte studieren sounds a little more like: yeah, it would be nice, let's see if I'll do it one day. Which doesn't mean that you won't, it's just not as strong as "wollen" I hope, that helped :)

You need to distinguish between mochten and möchten, as these are two totally different words. möchten = would like to wollen = want to