Is it plagiarism if only a short phrase or construct is the same? Suppose we have some text in a scientific journal article A. It is a verbatim copy of some text published in a related article B which is referenced by A, and this phrase is used to explain the same topic in both articles. However, the phrase itself is short, not a complete sentence and not very relevant (it could have been written in many different ways) but it seems the author of A has taken it from the original (B). Is this text plagiarism? I would rephrase it because it looks like a copy (it's unlikely it happened by chance given that the paragraphs in the two publications are related and the reference to B appears in a nearby paragraph) and that's not elegant according to my style and taste, but is there a general rule?
There is not a fixed set of rules for what is considered plagiarism (e.g., "5 or more consecutive, not quoted words"), although several guidelines are available. Unless entire paragraphs are copy-pasted, each case has to be evaluated on a single basis.

As for a partial sentence, it is likely not considered to be a bad case of plagiarism. 

That said, it depends on what the actual sentence is about. Are those 500+ papers plagiarizing each others because of that partial sentence? Certainly not. 

If the partial sentence was about a particular discovery reported in a particular paper, and that partial sentence was copied to a new paper as if the sentence belonged to the new paper, without a direct quotation.. that would likely be considered as a candidate for plagiarism. Quite for sure, it would be considered as plagiarism if a reference was missing, as well.

You might have some fun taking this Turnitin quiz on plagiarism.