When building a starship, you can choose from 9 different engine types. Although all engines can go Warp 9, the highest possible speed, cheaper engines are much less efficient at high speeds.
A common way of saving money is to equip the big ships that require many engines (a Basilisk requires 50 engines!) with a cheap type only, and build a cheaper ship with good engines that tows the big one.
The number of engines a ship needs is fixed. The engine count does not affect the fuel usage, though.