"supplement" is like many English words in that clarifying words are often left out: "The weight lifter was taking supplements." In that case, even though "vitamin" was left out, it would be assumed that we are talking about protein, vitamin, or some other supplements. Context is often very important in English. As an aside: 1) I wear my glasses when driving. 2) The glasses were in the dishwasher. 3) The glasses were on the floor. 1) refers to eyeglasses, 2) refers to drinking glasses, and 3) is ambiguous. In formal written English, we would write "eyeglasses" when we mean eyeglasses.

supplement = an addition/ an extra of something: The doctor said she should be taking vitamin supplements. The money I get from teaching evening classes provides a supplement to my main income. Sponsored = to support a person, organization or activity by giving money, encouragement or other help: The team is sponsored by JVC, so the players wear the letters JVC on their shirts. these definitions are taken from Cambridge Dictionary. Good luck!