"Ich möchte" is perceived as a more polite form of "ich will", so translating both to "I want" will lose important nuance and arguably be wrong.
Grammatically, "ich möchte" is Konjunktiv II of "ich mag", as you can see by checking a suitable dictionary. (Even though I think that it is mostly perceived as a form of the non-existent verb "möchten", we may witness the development of a defective verb here.) So it does indeed directly correspond to "I would like".