Travel is the general term to describe going from one place to another. We can talk about someone's travels to refer to the journeys he makes:
Travelling is also a general term which refers to the activity of travel:
Travel often crops up as part of compound nouns. Compare the following:
An expedition is an organised trip whose purpose is usually scientific exploration of the environment. You go on expeditions, just as you go on trips.
A safari is a trip or expedition to observe wild animals in their natural habitat in Africa, usually. You go on safari to safari parks. In days gone by, you might have worn your light cotton safari suit for this purpose:
cruise (noun and verb)
A cruise is a holiday during which you travel on a ship or boat and visit a number of places en route. When we cruise, this is exactly what we do:
A voyage is a long journey, not necessarily for pleasure, on a ship. We don't talk about voyages very much in the present time, but historically they were very significant: