The counties are administrative and there are bureaucrats who lead the county, but they are not titled, noble Counts and Countesses.

In Sweden, we also have administrative regions translated as counties, which are lead by someone I'd directly translate as "county chief" (as in "chief over this tribe") but they're anonymous bureaucrats a normal person wouldn't know about. (The common translation is the less exciting "governor".)

Not even true for the UK, which does have geographic peerages but they're not really linked to the county boundaries any more.

For some reason, the UK doesn't issue the title of "count", only "viscount". "Marquis" is linked etymologically to "marches", an old type of land allocation boundaries, but again not in practice.

The UK version of "count" is "earl".

No. To quote Hank Hill, we fought an entire war with England over that.