The Product Owner can track business value or other information on items in the Product Backlog. However, from a process perspective, only the sequential order of Product Backlog Items really matters. The sequence can be negotiated with the Product Owner, but that person is the sole and final arbiter of Product Backlog contents, including its ordering.
I won't bother with dictionary definitions here. Instead, I'll discuss pragmatic definitions in terms of successful Scrum implementations.
"Priority" is ordinal. It provides the Scrum Team with a sequence of items to work on in descending order.
"Value" is a subjective measure of how useful stakeholders think some feature will be. This is often financial (e.g. "How much money will this feature make our company?") or utilitarian ("How useful will this feature be to our target user?").
A Product Backlog Must Be Sequentially Ordered
In Scrum, the Product Backlog is strictly ordered by the PO-defined priority of the items it contains. This priority is solely defined by the Product Owner, although often with input from stakeholders and other members of the Scrum Team. An ordered Product Backlog sets out the sequence of items to be worked on, but that order can (and frequently does) change between Sprints or through negotiation with the Product Owner.
While value may impact the order set by the Product Owner, such as by placing higher-value items closer to the top of the Product Backlog, the "value" (if any) is never tracked on the Sprint Backlog because it's largely irrelevant (from a process perspective) to the Development Team. Discussions about value are usually between the Product Owner and stakeholders, and sometimes between the Product Owner and the Development Team during Backlog Refinement or Sprint Planning, but managing or assigning the business value of features (as opposed to incorporating the value statement of the viewpoint character from a well-written user story into planning and development activities) is not a defined responsibility for the Development Team.
The Product Owner is solely responsible for the content of the Product Backlog, and so they can certainly note business value or any other details they like on Product Backlog items if it helps them do their job. However, from a whole-team perspective, only the sequential order of items on the Product Backlog matters.