I would like to know more about the -아/어서 form.

Hello! While studying Korean, I came across the grammatical form '-아/어서,' but I'm not quite sure what it means and in what situations it is used. For example, in the sentence '시간이 있어서 영화를 봐요,' it seems to be used with a meaning similar to '~때문에,' but I'm curious about the exact usage. Also, I would like to know how this '-아/어서' form differs from other conjunctions like '-지만' or '-면,' or if it can be used in a similar way. For instance, I'm wondering if sentences like '시간이 없지만 영화를 봐요' or '시간이 있으면 영화를 봐요' are possible. I would appreciate advice from those who are knowledgeable about this grammar!