Distinction between present participle and gerund

One facet of the nominal fallacy, the error of believing that the label carries explanatory information, is the danger of using common words and giving them a scientific meaning. This has the often disastrous effect of leading an unwary public down a path of misunderstanding. Words like “theory,” “law,” “force” do not mean in common discourse what they mean to a scientist. “Success” in Darwinian evolution is not the same “success” as taught by Dale Carnegie. “Force” to a physicist has a meaning quite different from that used in political discourse. The worst of these, though, may be “theory” and “law,” which are almost polar opposites — theory being a strong idea in science while vague in common discourse, and law being a much more muscular social than scientific concept. These differences lead to sometimes serious misunderstandings between scientists and the public that supports their work.

Sometimes, it is difficult to tell present participle from gerund in some sentences

As seen above, it is not easy to identify what form two beings are

They seem to a present participle, but gerund is also possible in my opinion

Could you explain this for me?

theory being a strong idea in science while vague in common discourse

= Theory is a strong idea in science while it is vague in common discourse