Terminology derived from different theories of grammar often cause confusion. Since I'm regularly confused by what I think is "traditional grammr terminology", I thought I'd make a thread, as suggested in this thread. What I'll do is look at the example given in this thread in detail, using the terminology that makes sense to me, and pointing out other usage I'm aware of.

"The performer that sang the love song was my favorite contestant on the show."

1. Sentence level: Subject + Predicate:

Subject[The performer that sang the love song] + Predicate [was my favorite contestant on the show].

2. Constituent level:

2.1. Subject:

The subject is a noun-phrase. Subjects are normally noun-phrases, but they can also be dependant clauses, etc. I've heard clauses that appear in subject (or object) position "noun-clauses". I find this confusing; it does make sense in the context, but - to me - this priviledges "nouns" over "dependant clauses". I certainly see that it's more useful to speak of "noun-clauses" than to speak of "dependant-clause words" (instead of nouns), but the difference, to me, is a pragmatic one, not a logical one. That is: if I would accept "noun-clauses", I'd have to accept "dependant-clause words" for "nouns" (referring to the "function" not the noun). I find it easier to keep the terminology neutral on such issues, merely saying that both "nouns" and "dependant clauses" can appear in the subject position.

All this is irrelevant to the example at hand, as the subject, here, is a noun-phrase (a phrase with a noun at its head):

"The performer that sang the love song"

Performer is the head of the noun-phrase. Everything else expands that noun. The internal structure = [The] + [performer] + [that sang the love song]

2.1.1. "The" is a determiner, an article in this case.

To me, determiner is a function, not a form. Determiners are distinguished from modifiers, not from adjectives or nouns. I've seen "determiner" used to refer to a word class. I don't use it like that. Determiner is not a word class, but a slot in a phrase, in the same way that "subject" is a slot in a sentence.

2.1.2. "that sang the love song" modifies "performer". It is a dependant clause (more specifically a relative clause), in which a verb-phrase is introduced by a relative pronoun: [that] + [sang the love song].

sang = verb
the love song = direct object of verb (function) = noun phrase (form)

the = determiner
love song = compound noun, composed of two nouns, with "song" functioning as the head-noun (compound nouns are a special case of noun-phrases) and "love" functioning as a modifier (notice that I did not say "functioning as an adjective"; rather, I would argue that adjectives usually function as modifiers, but not every adjective in use is necessarily a modifier, and certainly not every modifier is an adjective).

2.2. Predicate: The predicate is a verb-phrase. The head of the verb-phrase is "was". "Was" is a linking verb, that links the subject with the subject complement: "my favourite contestant on the show", which is a noun-phrase in form, with "contestant" as its head.

2.1. This is the most interesting noun-phrase in the entire sentence. As it is, I'm unsure how to diagram this:

I don't hesitate to call "contestant" the head of the noun-phrase. Also, I don't hesitate to call "on the show" a modifier in function, and a prepositional phrase in form (with preposition [on] + noun phrase [the show] [=det + n]).

2.2. However, I'm confused about "my favourite".

On the surface, I would argue that "my" is a determiner in function and a "determinative/dependant pronoun" in form, while "favourite" is a modifier (of the head "performer") in function and an adjective in form.

But here I run into a problem:

I can easily find another noun-phrase that fits this mold:

"My little pony" --> "my pony" (det + noun), "little pony" (mod + noun). Notice how "my pony" and "little pony" combine into "my little pony" with little additonal meaning (I sense an added connotation of affection, but the denotations are pretty much the same).

However, "my favorite performer" does not work the same way:

"my favorite performer" doesn't seem to be a combination of "my performer" + "favourite performer". Trying to regroup the words, would make more sense, in my opinion:

"my favorite" + "performer": In this case, "my favorite" would be a "determiner phrase" (a term you hear more and more often lately), with "favourite" being a modifier of "my" rather than "performer"; by having the adjective "favorite" modify the pronoun "my", I qualify the relation my expresses. This interpretation makes sense to me.

Now, to people used to traditional terminology this will sound exceedingly strange:

First, I've heard "my" referred to as a "possessive adjective". Now, if I accept this either my argument above becomes way too complex to be practical, or it simply won't work: If "my" is an adjective, and "favorite" modifies "my", then "favorite" would have to be an adjective. Considering that the word "adjective" can alternately refer to function and form, this gets hard to puzzle out.

Second, calling "my" both a "determiner" and a "pronoun" must be confusing, even if I add the qualifications "determiner in function", "pronoun in form".

Sometimes differences in terminology create confusion. This is good, as trying to puzzle out what other people mean helps people learn more about grammar (I don't think a single theory of grammar can ever be "complete", in the sense that everything in language can be leaned from within it). But sometimes differences in terminology create misunderstandings. They can lead people to believe that the "other end of the line" is spouting nonsense. I've seen this happen on several occasions, which is a pity.

I hope my post helps people who use different terminology to understand the terminology I am used to, and enables them to help me understand their usage better.