It can, but it's not how it's used most of the time, so kind of a pedantic distinction.

And many do not even want to "move within a class" that much. They'd be satisfied to keep their job and retain the same constant purchasing power and ability to buy food, feed family, pay rent/morgage, year after year.

There's also cultural mobility which is different from economic mobility.

All are exemplified by reddit's Ohanian marrying one of the Williams sisters and thus having a either higher or lower social status, than either Ghislaine or Larry Summers, quite independently of how much cash they each have in the bank

I wonder if popalchemist would count the cultural station as something worth improving apart of the economic one