Engines are engines. However, there are some major differences between the engines that power cars and ones that power airplanes. The greatest difference is redundancy.
If an aircraft engine goes out at 3,000 ft AGL (above ground level), it’s not as though you can pull over to a cloud and call AAA. You’ll have to land somewhere — hopefully safely. That’s why most aircraft use engines with some redundancy. For example, larger aircraft have dual-magneto systems with two magnetos, two wires, and two spark plugs for each cylinder. You actually fly using both systems, but if one goes out you can switch over to the other and continue flying, albeit at slightly lower efficiency. Many light-sport aircraft use dual-magneto systems, too, for the same safety reasons.
Two types of engines can be used: two-stroke and four-stroke. Smaller engines such as the ones on lawnmowers often are two-stroke engines, simpler in design, lighter, and cheaper to buy. Four-stroke engines are more complex (your car has a four-stroke engine) and more expensive, but develop more power. Many ultralight aircraft are powered by two-stroke engines. Sport planes can be powered by either type of engine. Certified aircraft typically are powered by four-stroke engines. The decision typically is based on cost; two-stroke engines are simpler and less expensive.
The plan publisher or kit manufacturer will tell you which engines are approved for installation in its craft. Some of the leading aircraft engine manufacturers include Teledyne Continental and Textron Lycoming. Builders of light-sport aircraft engines include (alphabetically) Franklin, Gobler-Hirthmotoren (G-H), Jabiru, and Rotax. The most common models are from Rotax and Jabiru.
An important consideration in selecting a plane’s engine is the horsepower (hp) rating. Smaller aircraft require at least 80 hp with larger aircraft requiring as much as 300 hp.
Automotive and other engines have been adapted to experimental aircraft, which is the topic of thick books and lots of opinions. Among popular auto engines modified for aircraft are the Volkswagen horizontally-opposed air-cooled engines still readily available. If your plane’s plans call for a modified auto engine, do your homework and ask lots of experienced builders to find out what works and what doesn’t before investing time and money into this option.