I think support is potential; and maintenance is actual. E.g. "We only support version 10 of the software", meaning "we're only prepared to provide advice and maintenance if you're on v10". Maintenance is responding to an actual case or call where remedial action is necessary. That's true in IT and in other fields. That's the literal meaning of the words; there are also figurative interpersonal meanings, as in "my friends were really supportive of my marriage" or "he's a really high-maintenance guy, he takes up all my time and energy."