Do SaaS companies need both copywriters and UX writers?
Great subject, dangerous question. Answer is no.
SaaS companies need one person responsible for all messaging. That includes messaging used in the product UX and in marketing materials such as the company website and advertisements.
Designing your product and designing the marketing around it should come out of the same continuous ideation process.
There is no significant difference between an X SaaS copywriter and a Y SaaS copywriter, but there is something to be said for understanding interactive user experience - but this is true of all copywriting. Copywriting is 20% UX.
There is a difference among copywriters mostly when it comes to knowledge of industry, of customers, tastes, sayings, etc. If you market to several demographics, you might consulting several copywriters with, again, integrated product marketing oversight.