Q. How do I know I have reached the healthcare professionals Cochrane website vs layperson?

I have never heard of a distinction between a healthcare professional's version of Cochrane and a layperson's version of Cochrane.

I think this is what is meant ... access to Cochrane content is by subscription only. A "layperson" could find Cochrane through Google and see the citations for the reviews but could not read the reviews themselves.

A healthcare professional would have access, usually through school or work, to the subscription version of Cochrane. They would see the same citations as the layperson, but they would actually be able to access and read the content.

If this interpretation is correct, then the Library link is the healthcare professional's link, since we pay an annual fee and you, as a student, have access to the full-text content.