What is this part and if its broke off, does it affect function or safety?? THANKS

Disconnector, which forces a trigger reset between shots. Possible safety and function issue if it has broken off.

my other 84 does not have this??

Other model may be a system which doesn't use a disconnector, like a double action only or some other variant.

The one which has it, with your slide off and while holding the trigger pressed, press down on the tab as the slide would when cycling.  You'll feel a little click or snap and you'll be able to cock the hammer, but the trigger will not then release the hammer until you let it reset some, at which point that little tab will pop up again.  It is disconnecting the trigger from the hammer while the slide is cycling.  That small hollow in the slide gives it enough room to pop back up only when the slide is closed - otherwise the metal of the slide keeps it pushed down and prevents the trigger from acting on the hammer.

That's the firing pin safety deactivation lever. Your other one is probably an 84 and the one that has it is an 84B, BB, or FS. The disconnector is a hump on the trigger bar. If that tab is broken off your firing pin will not unlock and the gun will not go bang.

This. (The disconnector is barely visible just under the nose of the ejector)