This is a thing I've often seen, but I don't know whether it has a name and/or a story.
If we have some function $f(x)$, and for some reason $x(t)$ is also a function, they will omit the composition and only write $f(x) = f(x(t)) = f(t)$
Namely, they don't care about the actual function, but only about what variables it depends onto. This is also used when dealing with derivatives, they will write $$ \frac{\mathrm{d}}{\mathrm{d}t} f = \frac{\partial f}{\partial x}\, \dot{x}(t) $$ Does this notation have a name?