A combi (or combination) boiler heats both the radiators and the water as it passes through the boiler, this means you will get instant hot water and will not need to heat up a tank to get this. A Standard boiler has a separate water tank which is heated from the boiler through elements in the tank, you will need to heat this tank once or twice a day to guarantee hot water on demand, a hot water tank jacket can help insulate the tank so that the water remains hotter for longer.
A condensing boiler will be more efficient as it has a bigger heat exchanger that it uses to recover more heat from the burning gas, this will be the case for almost all boilers installed since 2005. If it was installed before this date then it is likely to be non-condensing.