Though ours are much different the base idea is there from the original story..
See they exist...but only if they can continue to steal items... you start missing a pencil or one part of a set of Jewelry? It was probably one of them...They prefer shiny and pretty things most of all...and they can get into any space necessary to aquire it...these cats become this way by being abused in life by their owner..so they are usually attached to the area their owner lived...some go above and beyond this and basically break the rules and detach themselves by stealing part of said owner (like How eyre has his former masters eye in a jar...) Enabling him to go anywhere to steal anything...
Most other Bakeneko are stuck close to the place where they had died and most others will not actually harm a human being...its considered taboo, and against the rules and any Bakeneko that harms a human will be hated by the other bakeneko. They do not share their items often....if at all...everything they steal is special.
Most Bakeneko hang out near shrines- due to the fact that there are things to steal because humans leave "offerings" and it keeps them alive just a little longer...though they dont get much energy from it...its still a good way to not die again.
Nekomata are pretty much the same... The only difference between the two (besides that Nekomata have two tails,) is that instead of how the Bakeneko can conjure imagery and terrify, Nekomata can do things a bit more "Physical" with the right amount of energy to spare they can even possess human beings or other living things... however this isnt something they really LIKE to do unless absolutely necessary, whereas the bakeneko like to cause trouble much more often.
Other Bakeneko/Nekomata at the Shrine