In practice, no. CR123 and CR123A name the same size of lithium cell, and the two labels are used interchangeably on packaging and in manuals. If your scope or light calls for a CR123, this Tenergy CR123A fits. A rechargeable 16340 is the same size but runs at a higher voltage, so read your manual before swapping.
It is. The Energizer 123 is Energizer's label for its CR123A-size lithium cell, and other brands print 123, CR123 or CR123A for the same battery. These Tenergy cells drop into anything that takes one, with PTC protection that guards against overheating and short circuits.
It depends almost entirely on the device. A thermal scope powering a sensor and screen goes through a cell in hours, while a light used a few seconds at a time can run for weeks. Tenergy's runtime figures aren't listed here, so carry spares on cold nights, when every battery gives up sooner.