Question regarding Witt's Theorem

Question

I am reading about Witt's theorem and the theorem in my book is formulated by considering two quadratic modules $(V, Q)$ and $(V', Q')$ that are isomorphic. This means that we can consider a singular vector space $V.$ However, are the quadratic forms $Q$ and $Q'$ the same? I can understand the book's proof if they are the same however, i'm not sure if saying the quadratic modules are isomorphic means that $Q$ and $Q'$ are the same as well.