Ok so it works like this...
"Game disconnected: you were kicked by an admin. Stated Reason: Hacking/Cheating."
^^^ This is fine. While you can't go on that server anymore, you can still play on others.
"Game disconnected: you were kicked by an admin. Stated Reason: Kicked by BF4DB.com - Reason: Hacking/Cheating."
^^^ This is a little worse. So now you are banned from any server that streams the BF4DB banlist. There are still plenty of servers you can join.
"Game disconnected: you were kicked by PunkBuster. Stated Reason: PunkBuster kicked player -------- (for --- minutes)... Violation [-------] #-----"
^^^ So this is really bad. You are now limited to UNRANKED servers and your account is permanently banned by PunkBuster. You can still transfer your game to another origin account with EA support and bypass this ban.
"Game disconnected: You were kicked by FairFight. Stated reason: 24 Hour Suspension - LvL2 Monitoring Active #UyTrG2" (Or #K98L9)
"Game disconnected: You were kicked by FairFight. Stated reason: 1 Week Suspension - LvL3 Monitoring Active #UYt8E5"
"Game disconnected: You were kicked by FairFight. Stated reason: Banned Code #J8Ytk2"
^^^ These are REAL bad. There is NO way to bypass these and depending on which code you got, you may have to create a new account and buy BF4 again.
"Game disconnected: You were kicked by FairFight. Stated reason: Restricted Area"
^^^ This is fine and you are safe. Just join back in the server.
Hope this helps.