I've wondered myself why "möchten" is often treated as a different verb instead of as a form of "mögen". My guess is that teachers are trying to avoid the confusion arising from the fact that both "mögen" and "möchten" work in the present tense, but have different meanings, don't you think? And then there's the problem with the past tense, because "mochten" looks so much like "möchten", but is actually the past tense of "mögen", while "möchten" just can't be used in the past tense. That combined with the fact that both "mögen" and "möchten" are usually taught quite early on, because they're so important. If they weren't used so frequently, then I suppose it would be easier to teach them as they ought to be taught: as different forms of the same verb. @Heinrich - "mögen" se usa con sustantivos: "Ich mag Kaffee". La traducción de "gustar + verbo" es "gern": "Ich trinke gern Kaffee".

I know that: Ich möchte bitte einen Kaffee trinken. I'd like to drink a coffe. Ich mag Kaffee trinken. I like drinking coffe.

Mochten is a verb of expression, also a modal verb. It can be used to express what you want/would like Ich möchte Käse- I would like some cheese Ich möchte ein Einzelzimmer- I would like a single room As a modal verb Ich möchte + infinitive of verb ( Ich möchte singen- I would like to sing.) Hope this helps.