The larger factor here is batteries are expensive enough that you don't want to mix and match. There is no reason your corded drill and saw need to be the same brand so you can choose whatever. However if your cordless drill and saw take the battery that means you don't have to buy as many batteries (or alternatively when your drill battery goes to the charger you take the saw battery instead of being unable to drill any holes).

Though people are starting to figure out that there are only a couple different batteries and so a cheap adapter means you don't need to buy all the same anymore.