In the English translation of “Adeste Fidelis”, *adeste *is translated as “come”. But later on in the same song, we get venite adoremus, which gets translated as “come let us adore him”. What’s the difference between *adeste *and venite?
Going by what I recall from my few years’ school Latin nearer sixty than fifty years ago: Adeste is an imperative form of the verb which means “to be present / on the spot”: Adsum from the same verb, means “I am here”. Adeste can, I think, be seen as bidding the faithful to be where the “bidder” is: doesn’t the verse go on to say Venite, venite in Bethlehem? (Venite adoremus comes later.) Venite: imperative form of the verb meaning “to come”; from being where the guy giving the instruction is, said guy is now bidding them to come with him from there to Bethlehem to worship the Christ Child. The wording “O come all ye faithful” is as it is, I would think in the interests of style and scansion rather than of strict linguistic accuracy.
"Venite definitely translates to “come” in English - I think* adeste* literally means something more like “be there”
nm
adsum is the opposite of absum (To be absent)
So, more literally, “Present yourselves, faithful!” Under the circumstances, “O come, all ye faithful” isn’t so bad.
Or be square?
I don’t see that in the carol anywhere … 
Be There or Be Square, All Ye Faithful
…ninjaed!