Change background from grey to pure white on jewelry photos

Gray is just a dimmer (darker, less bright) version of white.  And most cameras work similarly so it's not surprising changing the camera didn't affect much, as long as it is one that allows manual mode, not just full-auto.

One or more of these three situations is likely happening:

1)  The camera is set to "correct" the highlights and make them dimmer compared to the subject, as if you want to see detail in a wedding dress without the skintone being too dark.  Turn off any such auto-fix setting that effects highlights or dynamic lighting, so at least your camera is operating without mis-guessing what you're doing.

2)  You have the camera on Auto and it is metering for the background to be midtone, and the entire image is dark.  Increase the exposure compensation (EV) on the camera until the background is mostly white.  Now if the subject is an ok exposure and not washed out, you're done.

3)  Otherwise, you need to increase the lighting on the background compared to the lighting on the jewelry.   Add a light that is directed at the background and doesn't make the subject any brighter.

In any of these situations you'll have more freedom of control if the camera is set to Manual mode, ISO 100 (or something low) a high enough aperture for a reasonable depth of field, and a steady support so you can vary the shutter speed slower and faster without incurring camera-shake blur.

Now these instructions assume a DSLR or one of the newer, smaller DSLR-like cameras that allows full adjustments.  If you have a phone or ipad camera the amount of brightening and exposure adjustment may be limited, depending on the hardware or the camera app.

If you want someone else to look at a photo to see if it can be fixed in post-processing, then upload the original raw or original jpg to a large file hosting service like dropbox or googledrive or onedrive and post a public share link to it, here, and someone might be able to give their take in what needs changed.