Boilers

Boilers heat a fluid that circulates through piping, and heat is then transferred from the fluid to indoor air with heat exchangers. The fluid is normally hot water or steam - hot water delivers heat through fan coils, and steam delivers it with radiators.

In modern applications, hot water is considered the most cost-effective heating fluid for boilers. Steam heating is viable when a building uses steam for other purposes beyond heating, such as manufacturing processes. When a boiler will be used only for space heating, mechanical engineers will normally recommend hot water distribution.

Furnaces

Furnaces operate with the same energy sources as boilers, and the two equipment types are often confused as a result. The main difference is that furnaces heat indoor air directly, while boilers deliver indirect heating with hot water or steam.

Furnaces are simpler and less expensive to install than boilers, but consider that heat is delivered with forced airflow only. Water is a more effective medium than warm air for vertical distances, and hydronic piping is more compact than air ducts. Furnaces can also be noisy, since they require powerful fans to establish the airflow required.

In general, furnaces are more affordable than boilers, and can be used in buildings with an adequate layout for the corresponding air ducts. When the building involves vertical distances and zoned heating, boilers are the recommended option.

Space Heaters

While boilers and furnaces are used in central heating systems, space heaters are a common option when building areas need independent heating. Space heaters operate like furnaces with a reduced scale, since they heat indoor air directly with fuel combustion or electric resistance.

Electric space heaters are convenient and mobile because they use the building’s power supply. Space heaters have a low upfront cost, but a high operating cost.
Gas-fired space heaters are less expensive to operate, but they require a gas supply. They must be properly vented, since enclosed combustion produces harmful substances for humans - carbon monoxide in particular can be lethal.

Heat Pumps
Heat pumps are modern devices that can achieve low operating costs like combustion heaters, while having clean operation like resistance heaters. A heat pump uses a refrigeration cycle, just like an air conditioner, but the heat movement direction is reversed:

In an heat pump, the refrigerant is expanded and evaporated to gather heat from outside the building, and then compressed and condensed to release the heat inside.
For comparison, an air conditioner gathers indoor heat with refrigerant expansion and evaporation, to release it outside through compression and condensation.

Conclusion
There are many types of heating systems, and the recommended equipment changes depending on the budget available and building needs. Furnaces and boilers are the conventional options, while heat pumps are emerging as a viable heating solution.

In general, combustion heating achieves a lower operating cost than electric resistance heating, but heat pumps can often match the heating cost of fuels. When comparing furnaces and boilers, furnaces are normally the more affordable option, but boilers can adapt to more applications.