Hands up if you think the question has still not been answered here?
Yep me.
Difference between Continuous Descent Final Approach and constant angle descent profile.
Ludolf,
I think Jeppesen are responsible for introducing the term "Constant Angle Descent profile" and therefore causing this confusion. It is exactly the same as a CDFA in real terms. It is, as you describe, an aggregated descent angle that gets you from the FAF altitude/position to the MDA at the MAPt without having to level off in between or risk levelling off too early.
The other descent that starts well before reaching the FAF has all sorts of names including Continuous Descent Profile (CDP) and Continuous Descent Approach (CDA) and is a descent regime we should all try to stick to in order to save fuel and reduce noise over the ground. Most modern commercial jets have a FMS that calculates this for us (all the way from TOD) without much thinking on our part. Some terminal procedures explicitly call for it to be used whenever possible though in practice we remain governed by ATC descent clearances that "spoil it".