
The 3 to the right I presume you speak of...
Left is an early Franco circa 1910-12.

It was one that actually had this new invention...
The on/off sliding switch. These 2C sized were called baby lights because they were the ultimate in modern miniaturized flashlights. Very bright for their size with about 6 or 7 lumens cast over a wide area via the convex lens.
Rubber bodies held up better to those extremely leaky batteries of the day. It was a more durable light versus those "paper" bodied numbers of the day.
Soon that switch became obsolete.

Awe yeah! Technology.
By 1915 the internal slider was the norm for Franco. Also by 1915 police had begun to carry flashlights and metal bodies were becoming standard, although rubber bodies were still popular.
Right of the Franco are Eveready/Daylo lights called "Soldier Boys" circa 1917 to 1920-ish. Dark one is an enlisted mans light and the silver was an officer version. Eveready encouraged folks at home to buy them to donate to soldiers.
Again very bright and very portable for the period. A novel white reflector cast light much more consistant through the convex lens.
They were military issues to the lucky during the big 1. The switch combined a very effective belt clip that when not slid over the little 'ball' allowed signaling via that little 'ball'.
Ah, but soon after that became obsolete when the TL122A was released in about 1918 or so.

This one changed it all.
This one is a replica of a Bright Star.
A much more durable assemblage of parts n pieces, yet still pretty light and packable the much larger diameter right angle head cast a lot more light out front. The D cells allowed vastly improved runtimes and the switch system is still in use to this day.

Bright Star is given credit in 1925 but some old military re-actment supply sites swear they have photos of US soldiers carrying them in WW1.
The US Army and Marines still issue lights like these according to Fulton Manufacturing who supply them. It is reported that the Marines use their upgrade to LED kits that replace D cells with adapters and double A batteries.