Besides the points mentioned in other answers, a theorem or proposition is usually something whose main import is reasonably clear from the statement. A lemma, by contrast, is often a statement whose interest is less obvious until one sees it used.

So “if $X$ has diameter $< 1/2$, then the ring $St(X)$ is commutative” would be a theorem or proposition, depending on how important/difficult it is, since it’s clear to the reader what the statement means and why you might want to know it. But “if $X$ has diameter $< 1/2$ and the ambient braiding is sylleptic, then there is some $k$ for which all primary ideals of $St(X)$ are $k$-dense” is more likely to be a lemma.