See for me (at least) I would say PROPER copywriting is maybe writing a feature article for a travel website or magazine.Sorry to contradict you a bit on this but SEO and proper copywriting are the same thing these days - the 500 blog post model with keywords hasn't worked for a very long time now. (Average position 1 ranking page is now 2000+ words)
Don't get me wrong i'm sure people are still trying this as they are firmly in the past but it doesn't work - the move now is definitely towards high quality, long form, keyword optimised content for both SEO and what you're calling PROPER copywriting. (I'm Head of SEO for a marketing agency).
If i was trying to stand out and earn good money i'd be looking to develop this skill set as the way to earn the most money as people who can do this style of copywriting are in high demand.
SEO copywriting to me is ' write this article and insert this backlink naturally)
I agree the lines are getting blurred and that the demand is there which is why Content Conga works with no many SEO agencies now because they content at a decent price which sadly they don't seem to get from the likes of Fiverr these days paying as low as possible