In most fairly densely populated areas, the common US heating fuel is "natural gas." It comes out of the ground and takes little "cleanup" and it's pumped cheaply through pipelines with only an "odorant" added to make it easier to detect leakage.

In rural locations where there aren't pipelines for natural gas, "propane" use is fairly common, but is significantly more expensive. Where it's used, propane comes to the farm in a tanker truck, so the transportation costs are part of the reason it's more expensive than "natural."

The two "gases" are not interchangeable, although the equipment changes/differences required are fairly minimal if the equipment design permits swapping out the right parts.

"Natural gas" actually is a mixture of a range of molecular weights, but on average has significantly better "energy density" than propane, so it provides more heat per unit and is also significantly cheaper per unit. The price of natural gas has been falling recently, with the result that many coal-fired electrical generators have been replaced with plants that burn natural gas, simply because it's cheaper, but also because it evades the emissions cleanup devices mandated to be used soon. The emissions rules have been on the lawbooks for a very long time, so they're not traceable to any particular political party or administration. The demise of coal fired generating plants is purely due to natural gas being (currently) a whole lot cheaper and much cleaner.

In older communities there still are quite a few who use "fuel oil" which is sometimes called "diesel oil" or occasionally "kerosene," although there are differences between the products traditionally using each of the names. In the past, the term "coal oil" was used some, but almost never was a "correct" name and has dropped into oblivion in recent decades.

Some vehicles use a concoction similar to the home heating oil(s) (with a few more/different additives and slightly different refining) that's most commonly just refered to as "diesel." Most bio- processes for making vehicle fuels from plant materials produce fuels close enough to petroleum based "diesel" to be used as "biodiesel" with minimal effect on the machines that run on it, with the exception of about a 15% reduction in the miles per gallon and a slightly higher price per gallon at the pump. Refining the "bio products" to something suitable in non-diesel vehicles is too expensive to be practical at present, although ethanol can be extracted from some of them to be used as a gasoline additive.

Biodiesel market penetration might be higher in the US, but there are no diesel vehicles that can be legally imported from other places where they're used more due to emissions limits, and the demand hasn't justified more than token efforts to produce "home made" ones for sale here. Until fairly recently diesel fuel was significantly cheaper than gasoline, and you got twice the miles per gallon; but diesel here is now about 30%(?) more $ per gallon than gasoline and there are few choices for small vehicles that can use it.

"Gas" is a shortened form for "gasoline," the vehicle fuel called "petrol" in some other places. When there is the possibility of confusion, in US usage, "gasoline" would be the preferred term, but it seems many USicans have difficulty with words more than one - or sometimes two - syllables.

The number of "all-electic" new homes constructed in the US surged ca the early 1950s during a period of fairly low electric prices and higher prices for other fuels, but it's only recently that the advances in things like better heat pump efficiencies have brought the cost of electric heating close enough to natural gas costs to be really competitive, although new homes in higher price ranges have perhaps begun moving back to electric heating because it's considered a little "cleaner"(?) [you have to ignore the pollution at the generating plant to have cleaner at the end point] and likely(?) [just another crap shoot] to have more stable pricing. In newer communities with all the wiring underground, some argue that electric power is more reliable than other easily available forms, but that's a continuing debate.

As recently as the mid to late 1960s there still were people with coal burning home heating furnaces, and we had coal heat when I was in Boston (1963); but I can't say how many of that kind still remain in use. More widespread use of "pelletized" coal/coke and automatic feeders could have kept the usage alive, but it's pretty much unknown in places where there's easy access to natural gas.

For most homes in the US woodburning fireplaces are just a decoration, and as usually designed they suck about as much heat up the chimney as one gets in the house. They can be very efficient in a real heating system and are used in some places, but municipal codes in major cities discourage their use.

John