What are the words for the two parts of a round trip?

If you need to differentiate, they would be the outward leg and the return leg.

outbound |ˈaʊtˈˌbaʊnd| (adjective & adverb)
traveling away from a particular place, esp. on the first leg of a round trip: an outbound flight, flying outbound.

inbound |ˈɪnˈˌbaʊnd| (adjective & adverb)
traveling toward a particular place, esp. when returning to the original point of departure: inbound traffic, we have three enemy planes inbound on bearing two ninety.

Return is also adequate for the latter, as indicated by JeffSahol.

Parts of trips are legs, but that can also mean a trip where you had a layover (two legs in the same direction).