For example, do
Der Chef ist wütend.
Der Chef wütet.
mean the same thing?
I'm asking because the German for English Speakers site says
The present participle is a way of using a verb as an adjective, and in German it's only used right before a noun, as in "running water" or "barking dogs."
The first sentence above seems to be an exception to this. (There are other exceptions as well; the German Wikipedia article has more information. But I think I understand most of them, and I'm trying to limit the question to a single issue.)
PS. So I gather that the reason this is an exception to the rule given above is that the participle's meaning has diverged significantly from the original verb. You can use (present participle) + sein, but only if converting it to the simple present tense would change the meaning. Since wüten/wütend sein is an example where the meaning would change, wütend sein is allowed.
I think a similar case is sich schleppen/schleppend sein. You can say Der Film ist schleppend to mean that the movie is slow and boring. But Der Film schleppt sich seems to imply some kind of movement, which might be applied figuratively to the plot, but it seems unusual to do apply it to the movie itself.