Edit: Or do you mean that "polynomial progression" has an existing definition, and this definition is equivalent, but is a strange way of stating it? Or do you mean the definition as stated in the article is wrong / differs from the standard definition?
x^n + c where n, c are fixed and x goes 0,1,2,... with the progression
n^x + c
..the latter I'd call exponential progression
But yeah, seems to me these "shifted geometric progressions" are actually just a special case of a more general concept of a "polynomial progression".