In PCA and Factor Analysis, there is the term loadings, which refers to factor loadings (onto the original variable).
Does the term (original) variable loading (onto the latent factor) exist?
This is just a situation where terminology is being used interchangeably. It is more customary to say that a variable "loads on a factor" or principal component (PC), rather than a factor loads on a variable (PC). Specifically, however, it's the same thing. Loadings are correlation coefficients, essentially between an original variable $X$ and a factor or principal component $F$.
It's better to get into the habit of saying that an "original $X$ variable loads on a factor (or PC) with loading 0.65" (and not ever saying a factor(PC) loads on a variable).