Terms of use and terms of service name the same instrument, and no legal consequence follows from choosing between them. There is, however, one distinction the two phrases hint at which is worth keeping in the structure of the document: the rules that apply to any visitor reading a public page, and the rules that apply to somebody who has signed up and is being billed.
Visitor rules and account rules are different animals
A visitor never presses anything. Whatever you publish about copying your material, scraping your pages or relying on your content applies to them only as far as a browsewrap can reach, which is not far. An account holder pressed a button, and the record of that press is what makes the subscription, the liability cap and the dispute clause stick. Writing one document that treats both audiences as having agreed to everything overstates the first and hides the second.
How to structure it either way
Open with the parts that apply to everybody: who you are, what the site is, what the content is and is not, and the acceptable use rules. Then a clearly headed section for account holders covering sign-up, the plan, billing, renewal, cancellation, data and termination. That way the clauses that need real acceptance sit behind the step where acceptance is actually captured, and the ones that do not are not pretending.
The name to put on it
Use terms of service where there is an account and a subscription, terms of use where the site is mainly published material, and stop worrying about it after that. The important consistency is that the label on the button, the label on the footer link and the heading on the page all match, because your acceptance record has to name a document and it should name one document rather than three.
Questions people ask about terms of use vs terms of service
Is a terms of use enforceable against a visitor?
Only weakly, and only where the visitor had real notice. Anything you need to rely on should sit behind an action the user took and a record you kept.
Can one document serve both?
Yes, and for most small sites it should, with the account section clearly separated so the acceptance record points at something specific.
Does the name affect search?
Not meaningfully. Both phrases resolve to the same page for a reader looking for your rules, and the link label is what they are scanning the footer for.