They are different presentations of the same structure. The second one shows that the '6' is still there, it's just missing the first third of the event. It also shows that the '5' has been cut in half. The first presentation only shows the numbers with their 'onsets' intact. They're the ones you generally care most about, because sounds are triggered on onsets, so events without onsets don't make any sound.
drawLine expects a pattern of single characters, so it's parsing them as characters rather than booleans.
|> can only combine two patterns of the same type. So in this case I think the problem is that it's trying to parse "2 3" as a boolean pattern.
(0>⅓)-½ means an event that's active for the first third of the cycle, but is part of one that continues until halfway. In other words an event that would have gone from 0 to 1/2, when the end of it is 'missing'. In the case of 0-(⅓>½) the start of the event is missing.