Please don't get combi and condensing mixed up.
The Combi boiler does away with the hot water tank and gives you instant hot water. The hot water bit is internal to boiler so you don't have to worry about external wiring to give hot water, although the boiler may have the option to run as a combi it is not always used, as when used you can't add hot water from other sources like solar or back boiler, so it does need plumbing as a combi not just be combi type.
The Condensing boiler extracts more energy from the fuel, you can get both combi and condensing in the one boiler and you can get condensing with solid, liquid and gas fired boilers although rare with solid fuel, the main difference to use is it monitors return water temperature and adjusts flame height (not solid fuel) so you need to have TRV's fitted for it to work correct. It does not in theory need a room thermostat.
Out of interest although will not effect you, the solid fuel condensing has a water (or other) heat store because you can't turn down flame, the boiler runs at a set output throughout the burn. Then separate pump circulates water as heat is required.
From what you have said it would seem you have a Combi boiler, however as to condensing not so sure, the idea with condensing is the TRV controls the boiler, however the anti-cycle software simply does not work in the Summer, so you still need a wall thermostat simply to turn the system off. This is at the moment causing me problems. Once the temperature starts to raise you don't want the boiler to get house too hot, both for comfort and cost of running, if you have a room set at 17°C on the TRV and 18°C on the room thermostat then it would work, but 17°C is too low, heat from other rooms would cause the room to get too hot, and so switch off central heating too early. Go up a degree and then too hot in summer. Balancing the system seems impossible unless you have a thermostat outside to turn off the heating or use "If this than that" (ITTT) to monitor weather reports. Theory may be good, in practice it needs the house holder to turn off central heating in the summer.
