The Terra C is targeted more at gravel riding, with rims that have 25mm internal diameter and 32mm depth; the C38 seems more for road (or 'all road') riding with rims that have 21mm internal diameter and 38mm depth. Also, the DT 350 hubs are nicer than the 370, which is probably why the C38 costs a little more money.
Short answer: if you're mostly on pavement with a little bit of smooth dirt roads, get the C38; for gravel, get the Terra C. (Too bad you didn't ask this question about a week ago, when the Terra C was on sale.)
Upgrade pick is the Terra CL, which shaves a lot of weight -- mostly from the rims, which is good.