Let's say a user is banned on EL&U. Are they banned on all SE sites? Is there a different criterion for when they are banned for a different reason?
Generally speaking, a ban is only for one site and its meta, and if that site is the user's parent site for chat, they won't be able to participate in chat either. They are free to use other sites. ♦ moderators can only suspend a user on the site where they moderate.
If the user keeps on being annoying on several sites, or rather persistent on a single one, it's possible that they get suspended network-wide. It takes a Community Manager to do so.
(I assume you weren't talking about a question ban, which are always per-site.)
First of all: we prefer the term “temporarily suspended” instead of “ban” because in most cases it is intended to be a temporary timeout.
In addition to what @Glorfindel said:
Suspensions are intended to be temporary. There are cases where the staff wants to make a user leave and never come back but in most cases a suspension is used not as a penalty but to deescalate a conflict. See also this post for more info.
In these cases it wouldn’t make any sense to apply a network-wide suspension because the problem that caused the conflict is often only on one site (one post, one user).
Additionally some users are suspended on one site but very reputable users on other sites.
Therefore it wouldn’t make much sense to apply a suspension network-wise in every case.
A few users are not welcome on any site due to their behavior. In this case there are two options:
- Stack Exchange staff can run a script that suspends a user on all sites. This script is responsible for suspensions with the attribute “network-wide” and only these suspensions can be for longer than one year. This is done for users that have valuable content but were warned and suspended on multiple sites multiple times. Mostly they are used to “chase away” these users.
- Not really a suspension but users who have their posts deleted as spam will be fed into an anti-spam system called SpamRam (ok, unfortunately their data and not the users themselves). This comes with extreme rate limits and auto flags in the whole network.