Ping Sam Spade: DA versus DH on an ILS?

Sam and others, I have about 1,100 hours now with about 700 of those flown
after getting my instrument rating in the US back in 2003. Since then I have
flown IFR almost twice per week.

On a web-based aviation forum there is a general disagreement of the terms DA
(decision altitude) versus DH (decision height) when talking about an ILS
approach.

For those approaches that have published altitude minimums (typically ILS CAT
I or CAT II in the US), I was taught that the point at which one would begin
the missed approach is the decision height, or DH. However, in that aviation
forum there are a few who insist that this point is called the decision
altitude, or DA, and that DH is not valid for aircraft not equipped with
radar altimeter.

I did note that the current Pilot/Controller's glossary defines both DA and
DH as the point at which a missed does begin on a precision approach, but the
DA definition also includes the note about it being an ICAO definition.

Is this a case of semantics? Are DA and DH interchangeable when discussing
the point at which a missed begins? Or is there a more important distinction
between the two and I was simply taught inadequately?

--
Peter