For the case of a stationary loop, and a changing magnetic field producing a non-conservative electric field $E_{nc}$:
If the induced emf (${\Large{\varepsilon}}$) is due to both the change in magnetic field strength, and spatial change(due the magnetic field source's motion) an equation to model the sum of two effects is:
$${\Large{\varepsilon}}= \oint E_{nc} \cdot dl=\frac{\partial\Phi_B}{\partial t}=\frac{\partial B}{\partial t}\cdot S\cdot\cos(\alpha)+B\frac{\partial S}{\partial t}\cos(\alpha)$$
How is the final term ${\Large(\small{$B\frac{\partial S}{\partial t}\cos(\alpha)}}\Large{)}$ different than motional emf $v_xBL$?
I know in this case the loop is stationary, thus $v_x$ = $0$.
They seem to be the same mathematically, however, two different causes of effect.
Diagram:
