Firstly speaking boilers are divided into the following different fuel types:
Gas : Natural Gas (NG), Liquid Petroleum Gas (LPG), Hydrogen gas etc
Oil: Kerosene, Bio Kerosene, etc
Electric: Powered by mains electricity
Solid: Woodchip, pellets, coal, etc.
Then the boilers are further divided into the following types:
This due to small property sizes and lack of space has become a very popular choice for modern propeties.
Pros: Space saving heating and hot water in one appliance
Cons: If a critical part goes down, you can lose both heating and hot water. Requires larger gas pipes as the output is increased.
Hybrid Solutions: Combination Boiler with 1 Electric shower for backup purpose
This is commonly used with a Hot Water cylinder.
Pros: Hot water cylinder can be sized to demand with immersion heater backup.
Cons: Requires more space for the cylinder
Open Vent / Regular Boiler
This is commonly used in older systems with a central heating tank in the loft with possibly a cold water storage tank too.
Pros: Boiler size is small and where there are space constraints allows flexibility.
Cons: Open vent systems are liable for more corrosion than usual.
Combination Boiler with Store
This is a combined combination boiler with a hot water storage tanks.
Pros: Space saving with high hot water flow similar to unvented cylinders
Cons: The appliance can become more complex to fix and obtain system specific parts
How to decide which system is best use the following decision tree: