In high-altitude piston aircraft, what type of forced induction (boost) is used?
You can have either (turbo- or super-) or both (superturbo-), there is also the turbo-compound engine.

Most WWII aircraft engines had mechanically driven superchargers, and the turbosuperchargers (with intercoolers) were added to achieve desired altitude performance.
Modern aviation piston engines designed to run at high altitudes typically include a turbocharger rather than a supercharger. The change in thinking is largely due to economics. Aviation gasoline was once plentiful and cheap, favoring the simple, but fuel-hungry supercharger. As the cost of fuel has increased, the supercharger has fallen out of favor.
— Wikipedia [edited for context; citations missing from main article]

During WWII, two-speed two-stage intercooled superturbocharged engines were common.
(Frames from YouTube)
Compressed air via the exhaust-driven-turbine is channeled to a geared mechanically-driven supercharger. (The jet-engine must have had a laugh.)

You get the super part, which is a mechanically-driven compressor boost.

The turbo part, which is a turbine-driven compressor boost.

Intercooler for cooling the air.

The two speeds and stages are for low- and high-altitude operations. Otherwise the engine could blow at low-altitude.


A good example is the Wright R-3350 Duplex-Cyclone used on the Boeing B-29 Superfortress and other aircraft. Delivering up to 3,800 shp (2,830 kW).

Above is an example of having both, however as noted in the comments, superturbocharger as a term is nowadays used to describe a turbocharger.

Here's a declassified training film—from which the above frames were taken: Turbosupercharger: Master of the Skies (1943)