Imagine the boundary between trance and house to be a
gradient, rather than a solid line. The line is beyond blurry.
However, to make a few generalizations...
1. Trance tends to be mixed in an "orchestral" space. Think about the difference between a recording of an orchestra and a jazz band, in terms of "size" and "space." Trance instruments typically sound more like they've been "recorded" in an orchestral hall, rather than mic'ed up-close. This distinction doesn't really apply to a lot of recent progressive house, though.
2. Following the previous point, trance music conventions tend to be inspired by classical music (and rock power ballads, to be honest), whereas house tends to draw from jazz and funk roots. This is where the line really gets fuzzy, because there's a lot of "classical-sounding" house and "jazzy-sounding" trance. Especially recently.
3. In house, the bassline typically holds more
musical focus. There are strong basslines in trance, but it
usually sets up more melodic, high-register instruments to make the track what it is.
And now watch as everyone immediately disagrees with me.
