Come to think of it, a good example of the distinction are the NDBs (non-directional beacons) that aircraft use for navigation. They transmit, repeatedly, an identifier in Morse code, but the signal is an audio range frequency (somewhere around 500Hz) amplitude modulated onto a (radio frequency) carrier rather than being the carrier itself being pulsed.

One difference is that, if you tune an ordinary AM radio to the carrier frequency, in the CW case you’d hear nothing. In this case, you’d hear the tone as intended.