Hard to tell what all might have been replaced on the taller 24" frame.
Looks like 26" balloon (or middleweight) tire wheels on a non-balloon frame, but the front forks do not look like there is a lot of extra space for 28" tire;
(could just be the picture angle)?
Sprocket looks like a ladies or youths size by Snyder or perhaps others, but was it original?
Perhaps clean-up the bottom bracket joints area, could be Snyder (covered with crud)?
Perhaps post pictures of the usual locations of the serial numbers might be insightful?
Might lean towards a teens Davis built frame, (Sears Peerless or similar)?
Are the main tubes usual 1" diameter, or smaller for racer-type bikes (Westfield)?