First, "date" can be a noun or a verb. If I say "I have a date tonight," it doesn't imply anything about exclusivity or whether I've dated this person before. It could be with someone I've just met or someone I've been dating for a long time. People also talk about having a date with their spouse. "I'm dating someone," implies an ongoing relationship, probably exclusive, and that we have dated before and expect to continue dating. If I say "I'm in a relationship," it definitely implies an ongoing, exclusive commitment.