Are there publicly agreed-on standards or definitions of what constitutes peer review?
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."