Rotary, rotary engines the cylinders spin and the crank is fixed, radial, the crank spins and the cylinders (laid out in a radial format) are fixed.
The problem with rotaries is their higher torque induced roll and gyroscopic effect in aircraft due to the mass of the cylinders, not helpful in early light aircraft, this is why WWI rotary aircraft always banked one way to escape, they roll faster one way than the other; mind, their adversary also had the same fault/gain so it wan't much of an escape plan.
Cube for cube, radials win hands down in the power to weight race (hp/lb) as they're a much lighter construction and the large frontal area is no indication of sluggishness or slow speed, the Bearcat is up there with some of the fastest piston powered planes going, as is that Bristol thingy used in Korea by the RN.