Reply #25: The difference:

[Igel]

A.  [ [House] [Democratic [Conference] ] ]

versus

B.  [ [House [Democrat] ] [Conference] ]

The first is the House edition of the conference of the
Democratic Party members(presumably 'Party' is to be
understood, as is 'members'); the second is the conference of
House Democrats.  Each set of brackets [ ] shows boundaries of
words and phrases.

I find that [B] is what is properly understood by [A], in a
curious mismatch of form and meaning.

There's an option [C]:

C.  [ [ [House] [Democratic] ] [conference] ]

which would be the conference of the House Democratic Party,
but since there is no such thing ...

People act like a noun can't function as an adjective, then
they write things like 'House Democratic Conference', where
they must believe 'House' is a noun.  Chomsky would be
appalled--not at the phrase, but at the belief.