Generally, when you do this with an image editor like Photoshop, yes, this is destructive. That's because the software doesn't keep a JPEG-encoded version of the image in memory to write back unchanged. It decodes it to its own internal working format, and then re-encodes to whatever output format you want when you save. (It may be smart enough to use similar encoding options, but degradation will still occur.)

On the other hand, if you use software like Exiftool which is specifically designed to edit metadata and not actual images, no problem. This kind of software will copy the image data itself unchanged.

If you use RAW conversion software like Lightroom, which is meant for non-destructive editing of source images, your mileage may vary when working with JPEG files. Editing non-RAW files is not really the main use case of these programs, but they generally can, and then usually store any changes to the base JPEG as stacks of changes to apply (so those can be altered). That means they can know something like "oh, no image changes made" and not bother to re-encode anything. However, if you set export parameters to anything other than the exact same ones as the original encoding, that will probably force reencoding, which (again) will be lossy.

But that's a long paragraph to explain a special case. In general if you just want to change metadata, it's best to use a program designed for that purpose.