If your Workspace is using the Workflow feature, when you create a Space, it will connect to the Workflow you created it in by default. Any time you select that Space, it will switch you to that Workflow and show you the filtered stories for that Workflow only.
For example, if you create a Space while in the Product Development Workflow, it will automatically connect to it, and clicking on that Space will always switch you to viewing filtered Stories within the Product Development.
If you wish to connect or disconnect them from a Workflow, you can do so in the Saved Space's menu, under More Actions.
Any time you create a Space (and choose to disconnect it from its Workflow), it will just surface Stories that meet the Space's filters you have set in the Workflow you're currently viewing.
Filtering to Workflow States themselves will not be shared across Workflows, even if the name of the Workflow State matches.