They are very similar. You will have to supply a specific sentence that bothers you before I can say more.
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KrisBlueNZIn the sense "Don't bother me now" / "Don't disturb me now" they have very similar meanings, but both words can be used in other ways.
"It's no BOTHER" - "it doesn't BOTHER me; I don't mind"
"Don't BOTHER [doing something]" - it's not important enough to worry about, or to BOTHER WITH
"I can't be BOTHERED" - likewise
"BOTHER!" - rather old/posh U