A local ban is a ban that the server's admin applies on you. It's a ban from only that one server.
The opposite would be a global ban, directly from EvenBalance, the makers of PunkBuster. Those ban your key from all servers.
And somewhere in the middle, there would be bans from the Anti-Cheat communities like for example us(PBBans), GGC or PunksBusted. Those ban you from servers that stream to the AC community which placed the ban.
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/*Pisi*/