What grammatical roles do infinitives and participles assume when used predicatively?

A non-academic grammar site I was reading says:

A linking verb will always be completed by an adjective (a predicate adjective) or a noun (a predicate nominative).

…

A linking verb can only be completed by a predicate adjective or a predicate nominative (i.e., a noun or a pronoun). (source)

This, of course, is incorrect. I am thinking participles, infinitives, and predicative clauses which I am not sure fall under either one. But it occurred to me that I don’t know what the former two are called grammatically. I know in a sentence predicate a clause would be a predicative clause, a gerund a predicate nominative. And those mentioned are probably all predicative expressions.

She is running. (present participle)

She is stunned. (past participle)

The only thing she can do right now is wait. (infinitive)

So do these have specific names in grammar?