While most watch batteries may look the same on the outside
the inside can be very different depending on the manufacturer
Silver-oxide/Zinc
Years ago most watch batteries originally contained mercury which contained anti-corrosion properties. As mercury is an incredibly noxious substance, they were eventually phased out, and today have been replaced by batteries most commonly containing a silver-oxide alkali electrolyte, typically providing 1.55 volts.
Silver-oxide batteries require a specific electrolyte balance. If the solution isn't correctly balanced, then the batteries cycle life can be significantly shortened or the solution can corrode the seal causing the battery to leak, which can cause catastrophic damage to your watch.
Surprisingly, very few battery manufacturers can accomplish the correct balance.
Also the seal itself that connects the two terminals of the battery together while preventing a short. The material needs to be able to resist corrosion for years to prevent leakage.
All silver-oxide batteries have a shelf-life, and if stored without a load creating a power draw, the electrolyte will eventually become inert and the battery will fail.
Lithium-ion
Lithium-ion based batteries are generally used for higher power draw watches such as multi-function digital and GPS/Sports watches providing 3.0 volts.