Here are three similar coping saws. They are all marked "FULTON BF". Alloy Artifacts says that the BF was used as the manufacturing code for primarily tools from Japan made for Sears. However my third example is not from Japan. Going on the assumption that the thicker, heavier ones are older as newer ones using less metal made them less expensive to make and sell. These all take a 6 1/2" blades with pins.
The first example has a thick frame that measures .354" wide by .2" thick in the name stamp area. It has a 5" throat. The handle is made with a metal insert and ferrule that screws onto a 1/4-20 adjuster. The two levers for blade orientation have flats on both sides.
The second example has a thinner frame but has a 5 1/4" throat. The frame is .3" wide by .125" thick. The blade holders are similar to the first example. The handle has a red painted end. The two levers are smaller diameter and round.
The third example has a frame .263" wide by .125" thick. It has a 4 7/8" throat. The frame has a different design in that the ends where the adjuster go has been formed from round wire that is formed into loops. The adjuster end has a 5/16-20 thread and the lever protrudes on both sides. The other end looks like it was made from a 1/4" cotter pin with a groove cut in for the pin on the blade. This is marked "PAT. NO. 1929989". This would be D.E. Priest patent of Oct 10, 1933. This patent was assigned to Parker Wire Goods of Worcester Mass.
Comparing the name stamp area and the handle shapes, these all appear to have been made by the same company.
The above mentioned patent is not listed on Datamp.org and Alloy Artifacts does not mention Parker Wire Goods as a maker of a coping saw under the Fulton name for Sears.
Personal opinion: The first example has a stiffer frame and the blade makes a nice higher pitched sound than the other two, which seem much weaker.