The sprints are not "linked". The two projects are completely separate. Sprints are in the scope of a project.
A board is just a "view" on a set of issues. A board shows the issues selected by the filter. A board can show issues in just one project, or across multiple projects.
Cross-project boards can get confusing. An example might clarify what you're seeing:
Note the confusion potential with "Sprint 4" and "Sprint 27" being in separate projects. This is why I always coach teams to include the project key as a prefix for Sprint names. Thus:
Why is Jira like this?
Jira supports cross-project work at several levels. Epics, for example, can have child Stories from multiple projects. While a single Epic can only live in a single project, all the work under that Epic can fan out to multiple projects.
Since each Project has independent Sprints, the team working on that project can customize their work cadence. For example, the OPSA team might have one-week Sprints starting on Monday, and the OPSB team might have two-week Sprints starting every other Wednesday.
It's not intuitive (to those new to Jira) that the Sprint field is project-heterogeneous. Once you understand that OPSA-123 can be in an OPSB Sprint, things will make more sense.
Sprints will appear in a board based on these conditions:
1. The sprint was created in that board.
2. The sprint contains issues that are within the scope of the filter of that board.
When you modify the filter of the board, that results in all sprints that contain issues that are within that filter to now display in that board.
I think you are going to need to provide more details about what you are trying to accomplish between these two projects and two boards, to enable us to provide a better answer.
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