I was expecting to say there is no resemblance whatsoever, however, looking at the two images side by side, surprisingly, I think there are some similarities.
I think the major difference is the chin. She looks slightly double chinned in the painting and fine chinned in the image with the bonnet. That may be due to lack of skill of the amateur painter or the fact that she was younger and more full faced when that was painted. The sitter in the second picture is looking down a little so the angle is different.
Brows are slightly different but that could be explained by fashions* or the amateur painter trying to make her look more glamorous.
Still, though there are differences I think they
could be the same person.
*Added: By "fashions" I mean that the painter may have depicted features in a particular way as it was a fashionable look at the time, rather than the sitter physically possessing those attributes. For example, a high and fine brow might have been in vogue whereas in reality the sitter may have had lower brows as depicted in the second image, so the painter may have conformed to what was fashionable.
Using that logic I suppose it could be the case that all images of ladies of the time had a similar 'look' about them. They probably did.
It is often difficult to determine if two photographs are of the same person, and it is doubly difficult when you are looking at drawings, prints or paintings when there are so many other variables to consider.
