(click on pictures to enlarge)
The full sized examples are members of the Rex Manufacturing Co. family of pencils, but they are different from the others, in that they bear only the October 5, 1925 patent date, and the inscription is on the part just above the clip, rather than located on the cap.
See the Rex page for more information.
The small ringtop is a completely different design, resembling pencils from a variety of manufactures. Compare to the ringtop shown on the Eggens-Hambler page, for example.