Space propulsion is different from regular propulsion methods that deal with situations on the ground or in the air. It’s also different from launch propulsion which space propulsion methods exclusively deal with propulsion systems used in vacuum of space.
Before introducing different propulsion methods, there are couple of concepts that are really important related to the effectiveness of a propulsion system. The purpose of propulsion in the space is to change the velocity of a spacecraft. Since obviously that the more massive an object is, the harder to change its velocity, designers of spacecraft propulsion usually use the amount of change in momentum per unit of propellant consumed to compare the effectiveness. This is called specific impulse. It’s a different concept from the thrust which is the force moving a rocket through the air.
Essentially all spacecraft propulsion systems are reaction engines. These engines provides propulsion by generating chemical or physical reaction and expelling reaction mass. The most common engines are internal combustion heat engines. These kind of engines combust either liquid, solid or gaseous fuel with oxidizer within a combustion chamber. These type of engine needs a large mass of fuels. Rockets propelled by this kind of engine, such as monopropellant or bipropellant rocket, have relatively low specific impulse but high thrust.
The other kind of system, which is actually more suitable for traveling in the space, is electromagnetic propulsion engine. They don’t rely on the high temperature and fluid dynamics to accelerate the reaction mass, but rather accelerating the reaction mass directly by electromagnetic forces. The ion accelerating engine is the most common one among this type. These kind of engines are good that they usually carry little mass of fuels and they gain much greater specific impulse in the space.