Hello curious.k,
Is the second photo definitely your Great Grandmother? If it is then I would be reasonably confident that it is the lady in the first picture. The shape of the eyes, nose and mouth are all consistent.
Sticking my neck out, photo 1 is of a lady in her twenties or possibly thirties. The photo was taken around - say - 1910, which would make her birthdate around 1880. Does this fit with your Great Grandmother's date? In the second photo she seems to be in her 70's or even 80's, making the date of the photo 1950 - 1960. Does this sound feasible?
Yours
AJ