Trip is common as a noun that refers to a journey. It is a count noun, and can be singular or plural:

Bob and Lana met on a trip to the Caribbean.

Our family has taken many trips together.

Travel is common as a verb meaning to go from one place to another:

John travels a lot in his business.

Melissa has traveled all over the world.

Travel as a noncount noun is the activity of traveling:

Travel is broadening.

Travel is difficult in that region; the roads are bad and there is no airport.

Travel as a count noun occurs in the plural, but not in the singular:

In all your travels, have you ever seen such beautiful scenery?

He has accumulated 245 city maps for his map collection in his travels through 60 countries.

Travel does not occur as a singular count noun. Sometimes a speaker wants to make travel a singular count noun, as in:

INCORRECT: They took a travel.

INCORRECT: Jack is out of town on a travel.

INCORRECT: On my travel to Antarctica, I saw several kinds of penguins.