Your conventional central heating system is a convection heater: It heats up the air and circulates it (or just heats it up and it circulates naturally through the movement of warm air upwards and cool air sinking to the floor.
A stove that is a convection heater may be a pellet stove (which outputs hardly any radiant heat at all), or it could be a wood stove with an air spaced "jacket" that is designed to draw in cool air from ground level and output a plume of hot air above the stove, which will circulate on its own to locations that are cooler (except that warm air will not migrate downstairs from the level the stove is on). The Alderlea series of stoves from Pacific Energy are all convection heaters because they have the cast iron jacket around a welded plate steel stove. However, it should be remembered that there is still a lot of radiation from the glass in the door as well as the top of the stove and the stovepipe itself. So truth be told the PE stoves are a combination of convection heater and radiant heater, whereas a pellet stove with its very cool double wall flue is about as close to a true convection heater as you can get.
I personally prefer either a radiant heater or the combination approach. The big benefit with the combination approach is the small install clearances on the sides and back of the stove, and in the case of the PE, the underside of the stove too. The double wall construction does lower external surface temperatures, so you are much less likely to scorch anything near or under the stove. I can set my boots next to my PE T5 and even if the boots touch the outer cast iron cladding, no harm will be done (it won't melt the shoe laces etc. Now if you try that at the front of the stove, you will get a different result...