Activity feeds in main navigation menu are company wise. It will show notifications from all of the projects of an organization, where you are the team member.
Right navigation panel only shows updates from the selected particular Project. Select a different project on the board and click on right navigation menu > Activity, to see recent updates in selected project.
Tip: If you are a member of more than one organizations or companies, and want to see feeds for them. You can easily switch organizations by using the dropdown on the right side of the main navigation menu.
Note: This option appears on the menu, only if you are part of more than one organizations and using same user id and email.