The only difference is that Mendeley has a built-in PDF viewer with annotation. Of course since you can no longer share these annotations, nor export the pdf, that's all pointless.
Mendeley opens PDFs externally, but many PDF readers can create and save annotations.
In your second paragraph I think you mean to lead with "Zotero" instead of "Mendeley." And yes, I agree with that distinction. In practice, it hasn't been much of a problem (even though I do my work across OS X and Linux).
Mendeley opens PDFs externally, but many PDF readers can create and save annotations.