I have one project with 2 boards:
Is there a way to separate my tasks? I don´t want to see them in both boards.
You can amend the filter that each board is on to select the correct set of issues.
For example looking at your examples above it appears that you may be able to use the issuetypes field to distinguish between each board.
So assuming your project is configured in this way then you can amend the two filters as follows.
Scrum board add the following
issuetype in ("New Features","Improvements")
Kanban board add the following
issuetype in ("Change Request","Bug")
You will need to change the names of the issuetypes above to match your particular requirements but this should give you a start for splitting issues between different boards. You can use any field in the criteria to split issues between different boards. A common usage of this is to split the issues between different teams by using a custom field to hold the allocated team.