Are there publicly agreed-on standards or definitions of what constitutes peer review? It seems like a very difficult problem to discern whether a "peer-reviewed" journal is reputable. When a journal claims to be peer-reviewed, is there a commonly-agreed-on definition of what this means? Is there a publicly verifiable process to verify whether a journal is peer-reviewed?

This question mentions "vanity press" as a whole class of disreputable journals, and this question mentions Pubmed and Scopus as authorities on what constitutes legitimacy, but I can't find their standards anywhere. Scopus says they vet articles with an "independent review board," but I'm really looking for an answer about what they verify a journal does.
No, there isn't. Different journals/publishers will have different guidelines.

Here're some examples of publicly-published reviewer guidelines:


Wiley
Elsevier
PLOS One


To illustrate the differences, Wiley's guidelines say "What is the main question addressed by the research? Is it relevant and interesting?" (emphasis mine). Meanwhile PLOS One doesn't care about "interesting". To quote a testimonial: "I published with PLOS ONE because I love the idea that acceptance is based on quality of the work, not whether it's trendy or important in the eyes of a few editors."