There are no other classes. To call switching amps "class D", or to
create new designations for stepped B+ or stepped-bias designs
thoroughly confuses the original meaning [of classes].

So what would you call them ?

I wouldn't call them "classes", just a name describing how they work
or what they do.

That's why they're called a 'class' since everyone knows the output is
AB.

You COULD call them AB + G or AB + H but since it's a bit of a mouthful
most people don't. Rail switching or modulating is a bit technical for the
average buyer.

That's true, but if the average buyer doesn't have at least some minimal
understanding of how the circuit works, then the letter pretty much means
nothing -- other than as a way to distinguish to product, or (possibly)
impress him.

"Rail switching" is a good term. Here's a simple explanation for the
technically uninformed:

"A high-power amplifier requires a high voltage on its output stage. But the
higher the voltage, the hotter the amplifier runs. Because the highest
output power is rarely needed for more than a few seconds, this amplifier
uses a switched power supply, "cranking up" the voltage only when it's
needed. This lets the amplifier produce a lot of power without a lot of
expensive output transistors or huge heat sinks."

That's pretty good for a first draft.