Question on quadratic forms of dimension 3

Question

Let $V$ be a $3$-dimensional vector space over a finite field $\mathbb{F}_{q}$ where $q$ is odd. Suppose we have defined two quadratic forms on $V$ which have corresponding bilinear forms $(\,,\,)_{A}$ and $(\,,\,)_{B}$. Let $S_{A}$ and $S_{B}$ be the set of $1$-dimensional subspaces $\langle v\rangle$ of $V$ such that $(v,v)_{A}$ and $(v,v)_{B}$ are squares in $\mathbb{F}_{q}$, respectively. I know that the two forms are similar. Does this imply that $S_{A}=S_{B}$?