Terms of service and terms and conditions are the same kind of document under two names. No statute defines either, no court treats one as stronger, and nothing follows from which title you pick. What is worth deciding is not the name but whether the document describes a subscription, a sale of goods or the use of a free site, because those three need genuinely different clauses.
The naming convention, such as it is
Terms of service is the usual name where there is an ongoing service and an account: software, platforms, marketplaces. Terms and conditions is the usual name in retail and is the standard phrase in British and Commonwealth usage, which is why a store using a British theme or plugin often inherits it. Terms of use tends to appear on sites that publish rather than sell. These are habits of the trade, not categories with different consequences.
What actually differs, which is the content
A subscription document lives or dies on the renewal, the cancellation route and what happens to data at the end. A goods document lives on order acceptance, dispatch times, pricing errors and returns. A publisher's document lives on acceptable use, user content licenses and the disclaimer that the material is not advice. Naming the file correctly does nothing for any of those; writing the right clauses does. Where a business does two of the three, one document with clearly separated sections beats two documents that disagree.
Pick one name and use it everywhere
The practical cost of the question is inconsistency. A checkout that says you agree to our Terms of Service, a footer link labeled Terms and Conditions and a document headed Terms of Use are three names for one thing, and every record you keep of who accepted what has to reconcile them later. Choose the phrase your customers would use, put it on the button, the link and the document heading, and keep it there through every version.
Questions people ask about terms of service vs terms and conditions
Is one more enforceable than the other?
No. Enforceability turns on how the terms were presented and accepted and on whether the clauses are lawful, never on the title.
Which should an online store use?
Terms and conditions is the more familiar phrase to a shopper, and the document should be written around orders, dispatch and returns whichever name is on it.
Do I need both documents?
No, and having both is a liability: two documents on one subject will eventually contradict each other, and the customer will quote whichever helps them.