I've always considered that distinction you're describing to be between "tapping" and playing "touchstyle," and "two handed" being an optional adjective to toss in front of "tapping" if the mood takes you, but once again, this is just vague impressions. Anyway, i agree with your sense of the definition, that "two-handed" seems to be a little more technically intense than straight "eruption" licks. Who knows.
EDIT- actually, the only possible distinction between "two handed" and regular tapping is this- by definition, with "two handed" tapping, both hands are "tapping" notes onto the fretboard, while in traditional tapping, the pick may be used on some notes. for example, a sweep arpeggio with a tapped note at top- that isn't two-handed tapping, because you're using the pick to play all left-handed (if ou're a rightie) notes. However, a legato run with tapped notes in the upper register that involves many left-hand notes being "tapped" without a pickstroke when switching strings, even (IMO) if the initial note to kick off the sequence was picked, would be "two-handed" tapping, because both hands are "tapping" onto strings to start the string vibrating. I.E- a rusty cooley legato lick, descending towards the bass strings, with some tapped notes thrown in by the right hand. So maybe that's it...