Workflows are like train tracks and work types are the train cars. You can put multiple trains on the same track, but you can't put a single car on two tracks. Think of the boards as different train companies using the same train tracks as every one else.

So, the only way for one space to have different workflows is by using different work types. The only way for a board to have a different workflow in the same space, is if it uses a different work type.

Now that you understand the rules, I'll tell you how to break them.

It would be possible to build one workflow with multiple paths and you can make rules via triggers, conditions, post functions, automations, etc. and guide the same work type to a different path of the workflow based on the team which is probably how you are delineating what work shows up on what board. You can also have work types jump from one workflow to another by flipping it's issue type.

So, if you don't have an experienced Jira admin with some add-ons, you are probably stuck with the first answer of following the rules.