What is the difference between a statement and sentence in mathematical logic? I have seen many (GENERAL, BEGINNER TYPE) definitions, however, the actual meaning of a sentence I have yet to find, that is non-specific to a particular domain. This would be useful since a statement is defined in terms of a sentence and is one of the first concepts I am introduced to.

I would say most texts don't make a difference between the two. In fact: statement, sentence, claim, and proposition are typically all seen as the same thing: something that has a truth-value.
If a text does make a distinction, I suspect it might be between the syntactical expression that we use in order to express a claim, and the claim itself as more of an abstract idea, in much the same ads a number can be expressed in different ways: a numeral is what represent a number. Likewise, one could see a sentence as representing a statement or claim.
