Jim,
You left out Jeweler's saw frames. As a miniaturist and model builder I keep three frames on/near my bench at all times. This is the type of saw I always associated with as being a fret saw. Fret work being extremely fine saw work and usually done by hand held saw.
But as to defining a saw as fret or scroll by whether it is hand or powered or if it has pins in the blade or not is pretty confining. I had a treadle fret saw (so the name plate called it) which could be powered using a pulley mounted on the drive shaft. It could use either plain end blades or pin end blades. I could clamp a very fine jeweler's saw blade in it and by rocking the pedal, could do some really fine fret work. Clamp in a heavier 1/8" wide, course toothed blade with a pin in each end and I could saw (with a lot of huffing and puffing) out a scroll on a pump handle (rear spring support on a carriage) from 4" square black walnut. It also depends on which catalog it was advertised in as to whether it was listed as a scroll saw of fret saw. I also think the terminology differences might be regional or even different according to the country. I keep my spare tire in the trunk of my car.
For the fun of it, a little information from one of my old catalogues.
My 1896 N. O. Nelson Mfg.Co. of St Louis, Mo. Catalog lists four different power scroll saws. Two have wing nut chucks for the plain end blade. The No, 1 Victor came with a power drill attached for drilling a hole for scroll or fret work. This saw was foot powered and weighed 280 pounds. It sold for $40.00. The No. 4 Victor was a small bench mounted, steam powered saw using plain blades. It sold for $30.00.
Scroll saw No. 7 was powered by foot using a single pump type foot pedal. Pin blade. It only weighed 80 pounds and the price was reduced to $15.00. Such a deal.
Velocipede saw No. 2 Improved (no less) had a tractor seat and was powered like a tricycle. Pin type blades. With a drilling attachment it sold for $28.00 with out, $20.00.
Bill