Is Feeling tired a participle non-finite clause or a participle phrase

There is confusing information about a participle being treated as a non-finite clause by some sources and as a phrase by others.

Feeling tired is a present participle. Another example of the present participle: Removing his coat, Jack rushed to the river. Are these to be taken as non-finite clauses or phrases as in conventional grammar?

Similarly, how should Perfect participles and past participles be taken?