A combi boiler is a combined water and central heating boiler in one compact unit. There will be no separate hot water cylinder.
Conventional (sometimes referred to as traditional or standard) requires a separate hot water cylinder for storage.
A system boiler will require a separate hot water cylinder but no feed tanks in the loft. The boiler itself will have a water pressure gauge display as it is connected directly to mains water.
A back boiler is situated behind the fireplace. They are no longer favoured and are replaced by one of the other types when they expire.