So I've got this definition of complement from Wikipedia:
In grammar, a complement is a word, phrase or clause that is necessary to complete the meaning of a given expression.
and for subject complement:
In grammar, a subject complement or predicative of the subject is a predicative expression that follows a linking verb (copula) and that complements the subject of the sentence by either (1) renaming it or (2) describing it. It completes the meaning of the subject. In the former case, a renaming noun phrase such as a noun or pronoun is called a predicative nominal. An adjective following the copula and describing the subject is called a predicative adjective.
So as I understand it, subject complements are a type of complement.
There's various types though. Here is a link with some examples:
Pasting these examples below:
He is in the classroom. [PP complement] He is very clever. [AP complement] He is a teacher. [NP complement]
The "AP complement" is a subject complement (predicate adjective), and the "NP" complement is a subject complement (predicate noun), but the "PP complement" is not a subject complement, because prepositional phrases can't serve in the subject complement role. It is a complement though.
Have I got this right?