As an expat abroad you will still just be an expat abroad - equally an immigrant in the UK will still just be an immigrant in the UK
A basic difference will be that a Brit in an EU country will no longer be a standard EU expat, they will become a non EU expat
There may or may not be a reciporical arrangement that retains their status as was, or they will change to the status of a non EU immigrant/expat
There may be entitlements due to EU status that change, or that may be irrelevant due to residency
Many things subject to the terms under which we leave the EU, but that doesn’t mean Brits all get sent back and Europeans all get chucked out