Is there a difference between a union carbide 392 watch battery and a silver oxide 392?

I have an older LCD Quartz watch, it takes a union carbide 392 battery. I bought a 392 battery for it but it says silver oxide. After only a few months the battery died and I'm wondering why? I did take the battery out at one point and put it in an equally old watch to test, the watch didn't work. A week later did the same with another watch, which did work. At that time, when I put the battery back in the alarm started working on my watch. I used the alarm a few times, maybe 10-12 times. So could the fact that the battery says silver oxide rather than union carbide make it die faster? Or could it be that taking it out and putting it back a couple of times might have caused the battery to deplete more quickly? Thanks for any help.