barrd vs 86ing
Barred means still welcome in casino but no more BJ (or sometimes table games). 86ing means ejected from casino and warned not to come back or you'll be arrested for trespassing. Usually they read a written trespass statement (required by law) to warn you as they escort you out the door.
The trespassing only applies to that property (each casino in Nevada is incorporated separately (Bally's and Paris can be considered one entity...but Bally's and Caesars are separately managed and even have different corporate names...Caesars is "Desert Palace Inc d/b/a Caesars Palace). A manager from Bally's has no authority to 86 or trespass someone at Caesars just like he has no authority to issue comps or credit there.
All of the above does not mean that your trespassing at Bally's (or wherever) won't appear on your players file and that Caesars won't, upon seeing this, also trespass you. You should simply stay out of the sister casinos that trip and when you come back you should not use the same players card or should simply play anonymously.