I’m no twitcher but a quick look in a field guide lists both the European Robin (Erithacus rubecula) and the American Robin (Turdus migratorius) as part of the Thrush family (Turdidae) so they are related
But you can see from their scientific names that they are from completely different genus. Your “Robin” is a much closer relative to our Blackbirds (Turdus merula) than the humble Euro Robin.