What is a space heater? It's a commonly used term, and a surprisingly searched for term. I suppose the easiest way to define space heaters is a heater which is designed to warm a space up.
The difficulty is in that by space we tend to mean the air within a given area. So for example infra-red heaters - which heat what you point them at probably are not considered space heaters.
Good examples of what you might call a space heater are electric fan heaters which warm the air by passing it over some hot, resistive elements. Then there are the gas space heaters which burn gas in a jet, with a fan behind them - thereby transferring heat into the air as it burns. Of course the gas space heaters are also prone to giving off moisture and fumes and so aren't always the best choice.
Then we are on to the diesel space heaters, the cheapest and most common is the direct diesel space heater which works more or less like the gas version - exccept instead of burning gas it burns diesel. The more sophisticated space heater is what is commonly used as a marquee heater, the indirect diesel space heater . These are more sophisticated and burn in a steel chamber - keeping the fumes, moisture and burning embers out of the area you are trying to heat.
In conclusion, more or less any heater with a fan can be considered a space heater, what you tend not to think of as space heaters are the various forms or radiant heaters that are available, be they gas, diesel or electric powered.