What’s the difference between a ‘website copywriter’ and an ‘seo website copywriter’?

The difference is clearly in the SEO.

A website copywriter writes to engage your customers and help  you to convert sales.

An SEO Copywriter writes to engage your customers and help you to convert sales AND to help you rank more highly on Google.

In my mind, if you’re writing any website copy, you might as well get the most bang from your buck, and optimise for people AND Google :)