CR123A, RCR123A and 16340 are three batteries that are the same size but are different batteries.
The CR123A is a Lithium Primary battery that is rated at 3.0V. These are sometimes referred to as camera batteries because that is usually their primary use.
The 16340 is a Lithium-Ion (Li-Ion) Rechargeable battery that is rated at 3.7V. With a protection circuit, these are slightly bigger than CR123A batteries (16370). Because of their higher voltage (3.7V nominal, 4.2V full charge) they are not a direct replacement for CR123A batteries - they should only be used in devices designed for Li-Ion voltages.
The RCR123A is often used to refer to 16340 batteries, but this is technically not true. An actual RCR123A battery can be rated as 3.0V or 3.2V and are thus possible to use in place of CR123A batteries, if used correctly. The first few recharge cycles should be full charge and discharge to 'warm up' the battery from storage - best done in a device that can handle the voltage, such as a 16340 flashlight. After being warmed up, the battery can be charged to 3.0V and used in devices that can only handle 3.0V - a charger that reports the current charge voltage is best for this. Of course, if they will be used in a device that can handle the 3.7V of Li-Ion, then there is no need to worry about controlling the charge level.