A trip (n.) is the act of going to another place (often for a short period of time) and returning.
Use the verbs “take” and “go on” with trip. Always use trip (not travel) after a and the, and after possessives like my, your, our, their, his, and her:
A round-trip ticket is a ticket for going and coming back; and a one-way ticket is only for going.
The verb travel means going to another place (in general).
Travel (n.) can be used to describe the act of traveling in general: