No, they have entirely different physical dimensions.
A 371 watch battery
377 / 376 1.5v
SR920SW or equivalentlike 371
Watch Battery #371
I can't answer for all watches, of course, but it appears to be the 376/377 battery.
The Fossil AM 3242 watch typically uses a battery type 371 or 373, depending on the specific model. It's important to check the watch manual or consult with a jeweler for the exact battery type, as variations can exist among different models. Always ensure to replace the battery with an equivalent to maintain optimal performance.
Sony SR1116W
If you need a battery then there is nothing that can replace it.
Open the back of the watch, the battery is stamped with a number.
if the battery gets weak and useless, then you have to replace it...
how to replace a mitsubishi endeavor battery
how to replace battery