  In the framework of metric-affine gravity, we consider the role of the
boundary term in Symmetric Teleparallel Gravity assuming $f(Q,B)$ models where
$f$ is a smooth function of the non-metricity scalar $Q$ and the related
boundary term $B$. Starting from a variational approach, we derive the field
equations and compare them with respect to those of $f(Q)$ gravity in the limit
of $B\to0$. It is possible to show that $f(Q,B)=f(Q-B)$ models are dynamically
equivalent to $f(R)$ gravity as in the case of teleparallel $f(\tilde{B}-T)$
gravity (where $B\neq \tilde{B}$). Furtherrmore, conservation laws are derived.
In this perspective, considering boundary terms in $ f(Q)$ gravity represents
the last ingredient towards the Extended Geometric Trinity of Gravity, where
$f(R)$, $f(T,\tilde{B})$, and $f(Q,B)$ can be dealt with under the same
standard. We also compare and discuss about the Gibbons-Hawking-York boundary
term of General Relativity and the boundary term $B$ in $f(Q,B)$ gravity.
