Different captions for the same image in multiple galleries. Edit Image in Gallery locally

The caption is stored in the image data. The only way to achieve what you require is to use multiple copies of the image and change the image data on each image. To better understand image data go ahead and download an image to your desktop then right click it, go to properties then the details tab. this is where the image meta data is set. WordPress does has a few image meta settings but does not cover all of them. I feel its better to compress images on a pc or mac using Caesium image compressor then once compressed then change the image meta on your PC or mac. Google does not like sites to use the same image multiple times on different pages as this should be put into a sprite image. Sorry to be the barer of bad news but I hope it helps you better understand image meta.