yes 3 kinds of rechargable 123 type cells.
1) regulated li-ions that are about 3.6v max, and dont usually overdrive a light
2) li-ions both protected and unprotected , max at 4.2 will overdrive lots of single 123 light, unproteced are dangerous when used incorrectally. li-ion cells are often designated by size numbers 16340.
3) the new safer Li-FePo4, which is different chemisty , so its lower voltage like regulated li-ion, but not as much total capacity. really safe chemistry safer than lithium or li-ion (so far)
(so far) most all of the rechargables run for about 1/2 as long as a throw away lithium 123. li-fe even less by a bit.
most of them use the same basic RCR123 designation the R meaning rechargable, all 3 different types use a different charge style, so they are not nessisarily compatable among chargers.
as of yet no ni-mhy LSD type of 123s, it was discussed, and most the people here figure it would not be good capacity.
Rechargables are Great, if your around some sort of power, or even solar power. a person could save from 25-100$ with them, if they were using a lot of 123 cells regularly.