The thread posted by Thefo is helpful, but you still kind of need to know what you're looking for to make full use of all that information. Here's a basic breakdown:
We generally speak of batteries in terms of their internal chemistry. Some of the names have become colloquial rather than functional but regardless, the names you are most likely to hear are:
- Alkaline Batteries - These are your typical Energizer, Duracell, etc... batteries that come in sizes like AA, AAA, C, D etc. They are one time use (not rechargeable) and operate at a nominal voltage of 1.5 volts.
- Lithium (primary) Batteries - These are relatively popular and available to consumers just like Alkaline batteries. The lithium chemistry allows for a typically higher capacity than an alkaline battery and are often recommended for higher drain electronics. In
addition to the added capacity, we like them because they operate nominally at a wider temperature range (especially at lower temperatures) than alkaline batteries. The downside is that they are usually more expensive if purchased at a typical consumer
outlet.
- NiMH Batteries - These are rechargeable batteries. They are not necessarily drop in replacements for all gadgets because of their lower (slightly) functional voltage of 1.2 volts. They will however work for most flashlights you are likely to encounter on this
forum that are designed to take "AA" or "AAA" batteries. One disadvantage is that these cells have a certain degree of self discharge, meaning that when stored (not in use) they will gradually lose a charge. Depending on your application, this may not be a
problem but it is usually frowned upon by flashlight users who want to make sure their lights are ready if and when they are needed.
- LSD NiMH Batteries - Low Self Discharge NiMH batteries are a relatively new battery type that leverage the advantage of rechargeable NiMHs but have a much reduced self discharge rate. Sanyo Eneloops are a popular example of these batteries. This are
basically the go-to battery for flashlight users who want high capacity, recharge ability, and long(ish) storage life but don't want to mess with Li Ion batteries.
- Li Ion Batteries - Lithium Ion generally describes a whole class of batteries with various cathode materials. The most popular one you will encounter around here are LiCo02. When you hear someone say "14500 Li Ion" or 18650 Li Ion this is likely what they
are referring to. These cells are rechargeable, and have a VERY good shelf life (very low self discharge), and operate at a higher voltage (~4.2v) which make them ideal for the high output lights many users on these forums own. The disadvantage is that
these cells can be over discharged if not watched carefully which can damage the cells and potentially result in the batteries popping/exploding. If proper care is used, this is unlikely but many users are fond of "Protected" versions of these batteries which
have a small internal protection circuit which will shut off the current from the cell when it is discharged beyond a certain point.
- IMR Batteries - Technically, these too are Li Ion batteries (just with a different material as the cathode). They have the same voltage as the batteries listed above but they are considered safer because of their ability to be safely drained more rapidly by
very high consumption devices. These are not protected because they don't need to be. They generally offer slightly reduced capacity relative to the LiCo02 batteries of the same size.
Some specific notes:
- The number in a battery's name actually describes its dimensions. The first two digits describe the diameter of the cell and the next two digits describe the length. You mention a 14500 in your OP. That is the equivalent of a AA cell; 14mm wide and 50mm
long. Popular sizes are as follows:
- 10440 (AAA)
- 14500 (AA)
- 16340 (CR123a)
- 17500
- 17650
- 18500
- 18650
- 26650 (C)
- 32650 (D)
Please note that the Lithium Primary CR123a battery which is very commonly used on this forum is not 1.5 or 4.2 volts but 3.0 volts.
Regarding your choice of a light, the 4Sevens Quark AA is a great light. One of the best parts about it in my opinion is that it accepts a wide variety of batteries. It will run on an alkaline AA (though most forum members would discourage it), a lithium primary such as an Energizer Lithium cell, a rechargeable NiMH such as an Eneloop, or a 4.2 volt Li Ion cell. Note that you will see a substantial increase in performance using a Li Ion cell vs other chemistries. I own one myself and it performs magnificently on an AW Protected 14500. There are other brands of Li Ion cells available from various retailers (many connected with the forums here) but I have always had good experiences with AW brand cells.
Hope this was helpful and Welcome to CPF!