Power tool batteries are very much tied to the tool. Manufacturers tie their tools to their own line of batteries. After market options are severely limited.
Lithium-Ion battery technology is the market leader at the moment. The other technologies are mostly inferior in one or more ways, but cost considerably less. The most improtant consideration is to purchase a battery that delivers enough energy to drive the tool.
In most cases there are only one or two batteries that will fit a particular tool. The search feature of Hingmy will help you narrow down your choices.
If the choice comes down to a larger, longer lasting battery, and a smaller battery don't automatically jump to the larger battery. The balance of your tool changes depending on how heavy the battery is. It makes sense to install the smaller battery in lighter tools that have been designed for the smaller battery.
Adapters exist that let you use batteries from one manufacturer with tools from another. Unfortunately these devices throw off the balance so much that brand name batteries are almost always the best choice.