Size 675 cochlear batteries and size 675 hearing aid batteries are the same size and are interchangeable. However ...
The cochlear batteries have been optimised to cope with the higher power drain in a cochlear implant processor. This is usually done by adding an extra air hole to allow more air into the battery.
Depending on the hearing aid, if you put a 675 cochlear battery in hearing aid it may sound flat compared to using a normal 675 hearing aid battery.
Depending on the implant processor and map, if you put a normal hearing aid battery in a implant processor the high power drain will either cause the implant to beep constantly as if the battery were about to be flat or it simply cuts off as it cannot cope with the power demands. For this reason, it is most likely the battery life of a 675 hearing aid will be shorter than a 675 cochlear battery.
Some implant processors, such as those from Medel, are designed to use normal 675 hearing aid batteries.