Does "contains only" imply "contains"?
My view is that vernacular would consider that S is not empty,
i.e. $\emptyset \neq S\subseteq T$, while mathematical language would
consider that S can be empty, i.e. $\emptyset\subseteq S\subseteq T$.

Lay people do not speak of empty sets, while mathematicians are
aware of their role in their work.

That means that the sentence is not ambiguous, but the meaning depends
on the community where it is used.

Of couse, people aware of the two readings can play games with it. But
that is yet something else.

You may notice that I did not specifically mention English, because
the same is probably true of many "languages".

To think that English  (or German, or French) is a well defined language is
unrealistic. Actually, I doubt you can find two people who
agree on what is English and the meaning, or on the ambiguity, of its sentences,

It might be interesting to ask the linguists.