Sources close to Jake tell TMZ ... both he and Zayn were staying at the same hotel in Vegas over the weekend, and they were even on the same floor with rooms next to each other. We're told that after the fight, Jake was making his way back to his room when he spotted  Zayn and co. getting off the elevator. Jake asked if they were partying, plain and simple.

Now, what happened next is a little hazy -- because what we're hearing from Jake's side sounds much different than what we've heard from Zayn's side of things. Per our Jake sources ... Zayn fired back with a rude line ... "IDGAF if you have a good night."

We're told Jake was taken aback by the abruptness of the remark, but he let it go and just went to his room and kept raging with his brother, Logan, and their friends. At the fight, Jake almost got into it with a member of the crowd ... seems it was that kinda night.

Anyway, we're told Jake ran into Zayn again in the hotel hallway a bit later and attempted to clear the air about their spat. But, according to his account, Zayn got even testier ... yelling at Jake and asking "Who the f*** do you think you are?!" It didn't end there.

Our sources say Zayn even challenged Jake, asking if he wanted to "test" him. Doesn't sound like things got to that level -- but clearly, the feud spilled onto Twitter ... and roped in Gigi.

She stepped in on behalf of Zayn and shut Jake down, calling him "ugly" and "irrelevant." We're told Jake doesn't hold a grudge, acknowledging they were both in the wrong ... and that booze was likely a factor on both sides. The implication ... Zayn was drinking too.

It doesn't appear that people close to Zayn agree with that characterization though -- we're told Jake was drunkenly pestering Zayn to come party, even though Zayn had already said no. No mention of ZM boozing -- just JP. In other words, this was a one-way street.