Masonry vs Hard Coat Stucco

I was always under the impression that the terms masonry stucco and hard coat stucco were somewhat interchangeable. Somebody recently questioned this when I mentioned it and it got me doubting myself…

My understanding is that hard coat stucco is applied to a metal lath over a substrate, but can also be applied directly to concrete block construction, i.e. masonry stucco. Is this incorrect?

Stucco Installation Standards

Frequently Asked Questions About Stucco Applications

Google hard vs synthetic