What is the difference between a full service airline and a budget airline?

A budget airline is focused on providing discount service. There are no frills, no amenities, no free food, no alcoholic drinks, no movies, etc.

With a full-service airline, you pay more for the tickets, but the arrangements are more comfortable. Food and drinks are included in the ticket cost, there may be movies on-board, there may be Alcoholic Beverages available, the seats tend to be assigned, etc.