What's the difference between 'obtain' and 'gain'?

One syllable.

Actually obtain implies a previous effort to get, gain does not.

Obtain and gain are given as meanings of each other by some dictionaries. There is not always an implication of prior effort when using 'obtain.

Oxford Advanced Learner's Dictionary:

gain: to obtain or win sth, especially something that you need or want.

obtain: to get something, especially by making effort.

Merriam-Webster:

obtain: to gain or get (something) usually by effort

Note that neither 'especially' nor 'usually' means 'always'.