What is the "right" name for this Diophantine equation? $ a_1 x_1 + a_2 x_2 + \dots + a_k x_k \equiv n\pmod h$

Question

I am not able to find a clear answer to what is the right terminology to refer to this type of equation: $$ a_1 x_1 + a_2 x_2 + \dots + a_k x_k \equiv n\pmod h\,. $$ where $a_i,x_i,n,h(\neq0) \in \mathbb{Z}$.

Clearly this is a Diophantine equation as we can express the $\mathrm{mod}\ h$ as and extra term $\gamma\cdot h$ on the right/left hand side. But given the modular arithmetic, should this be called, to be more precise, a linear multivariable congruence equation? Or should this be called a linear modular Diophantine equation? Or a linear Diophantine equation in modular arithmetic?

Thanks!