It looks like Project - View and Project - View management Access are working as same when the user has Resource - Hard book access to a user.
The description of the access right Resource - Hard Book - All in Clarity states:
"Allows user to Soft or Hard book all resources to an investment that the user has been granted view management rights."
Based on that description should both Project - View and Project - View Management allow the user to update the team on a project?
Release : All Supported Releases
Both Project View rights will give the user access if they have Resource - Hard Book or Resource Manager (auto) access to the user:
The description only mentions Project - View Management as it's the one access right available at the global level (Project View is not).