"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"][1], as you can see by [checking a suitable dictionary][2]. (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".


  [1]: https://de.wiktionary.org/wiki/m%C3%B6gen
  [2]: https://de.wiktionary.org/wiki/m%C3%B6chte