Yeah, huge difference between not being able to keep good time and not being able to start at the "right" tempo.
A buddy of mine used to be in a band where there was constant tension between the drummer and the singer/keyboard player over tempos.
Both of them were great musicians, but also had short tempers and didn't like to compromise.
The drummer wanted the option to play songs a little faster or slower at gigs, based on reading the crowd or whatever, but the singer was really strict about how fast/slow he could do certain songs.
They almost got in fist fights about it multiple times until the two of them sat down with a hand-held metronome and agreed on an exact bpm for every song in the set. The tempos would get written on the set list next to each song and the singer would walk over, whip out the metronome, dial up the click and hold it up to the drummer's ear before the songs. It was ridiculous. The band fell apart soon after, despite having 5 great musicians in it and getting as many good paying gigs as they could handle.