The majority of batteries in the world are made either in China or Japan. There is a very wide variety in the quality of batteries. The better batteries come from Japan and those manufacturers are leaders in the industry - Panasonic, Sony, Samsung, and Sanyo.
AW is a distributor in China who purchases batteries from Japan, puts them through strigent testing, and uses the best ones as the AW brand. For years AW has had the reputation of being the best consistant battery your could buy.
Not all batteries made are created equal. Manufacturers use a quality control process to test their batteries and the lesser quality batteries are culled and sold off to other distributors, the majority of them being in China. These second tier batteries are re-wrapped and sold by the distributors. Still other batteries are harvested from old laptop computers, re-wrapped, and sold as new. Most of the so-called generic batteries (no brand name or off brand name) fall into this category. The battery trade is a very competitive market and many of the distributors are not very ethical. In fact, some make counterfeit AW batteries, so buyer beware.
There are no standards governing battery advertising. Manufacturers and distributors can put whatever specifications they wish for their batteries, and a few of them over-state the specs to make them more appealing to customers against the tight competition of other battery manufacturers.
The batteries which we use in mods and e-cigarettes are lithium ion batteries. There are different chemistry types of lithium batteries.
ICR - these are the cobalt-based protected Li-ion batteries. Typically have high mAh ratings, but low amp ratings. A flamable chemistry which can vent hot gas and flames, with the possibility of explosion if the gases are contained in a metal tube.
IMR - these are known as Li-Mn, lithium-manganese, safe chemistry, high drain, and unprotected batteries. Inherently safer chemistry than ICR batteries. Lower mAh but higher amps for high drain applications. Preferred over ICR batteries. May still vent gas during failure, but not as dramatic as an ICR battery.
hybrid - a mix of ICR and IMR chemistries. Retain both high drain and high capacity qualities of ICR and IMR.
Different battery chemistries are indicative for different mod applications. For instance, regulated mods require a high drain battery for their buck boost/pulse circuitry. Mechanical mods using a Kick or RBA require a high drain battery. Sub-ohm vaping requires a high drain battery with ultra high amp specs.
If you see a pattern there, it should be apparent that ICR batteries are no longer applicable for most applications in mods. High drain, safe chemistry batteries are recommended.
Battery Basics for Mods: IMR or Protected?
Deeper Understanding of Mod Batteries