As far as I am aware, these forms all mean take/bring (depending on the frame of reference).
Is there any difference in meaning or usage between 가지고 오다/가다 and 가져가다/가져오다? Or are they entirely interchangeable?
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The verb '가지다' conjugates to '가지어-' which can be contracted to '가져'. '가지고' is a contracted form of '가지다' + '고' (and), connecting two verbs.
They are two different ways to connect the two verbs '가지다' and '오다'. Both are commonly used, and I believe they are entirely interchangeable.
It's similar thing like '안녕히 가세요.', '안녕히 오세요'.
가다 = go 오다 = come
가져 consists of '갖다'+'아/어' or 가지고 consists of '갖다'+'고'
'아/어' and '고' are used to have two verbs.
가져 오다 = bring 가져 가다 = take out
this video may be helpful.