What's the difference between 좋아해요 and 좋아합니다?
좋아해요 = polite, informal
좋아합니다 = polite, formal
It's the level of politeness. The first one is just polite and the second one is formal polite (a higher level of politeness).
i think 좋아합니다 is more formal/polite than 좋아해요.
좋아해요 is informal polite and 좋아합니다 is formal polite.
Informal versus formal
It means the same thing, but with different moods (formal, informal, etc.) It's best to familiarize yourself with the different forms of the same word since they change depending on the situation (who you're talking to, etc.)
좋아합니다 is more formal than 좋아해요.
The level of formality/politeness. That's literally it.
From my experience, the former is used more commonly. The latter is super formal and you would use it in situations like interviews
One is polite and the last one is formal. Longer the ending means the more formal.