This is one of the differences between UK and US English. In Britain, the term "eye doctor" just isn't used. It's of a type with legislator vs law-maker; it's

This is one of the differences between UK and US English. In Britain, the term "eye doctor" just isn't used. It's of a type with legislator vs law-maker; it's only really in the past few years that politicians in the UK have occasionally been referred to as law-makers.