In a manual transmission, matching engine speed to wheel speed when downshifting is called rev matching. The driver briefly raises engine rpm before releasing the clutch in the lower gear.
When a car is moving, a lower gear requires the engine to spin faster at the same road speed. Pressing the clutch disconnects the engine from the wheels, so the engine can be below the speed required by the selected lower gear. A quick throttle blip brings it closer to that target before clutch engagement, reducing the jolt and unnecessary clutch wear.
Rev matching is the general action; heel-and-toe is a particular technique for doing it while braking. Double clutching is an older or specialized method in which the clutch is released in neutral between gears, allowing the driver to match transmission speeds as well as engine speed. Float shifting means changing gear without using the clutch, not matching rpm during a downshift.
Some modern sports cars automate the throttle blip. Nissan’s SynchroRev Match system, for example, uses sensors and electronic throttle control to perform the operation for the driver.