My understanding is that animated JPEG-XL is an image-only distribution format (like animated GIF), whereas Motion JPEG is a compressed media standard used during capture/production that supports interlaced video, etc. In other words, the similarity mostly ends with the name.
History truly is a circle: We replaced animated GIFs with soundless AVC/HEVC/VP8 videos for storage efficiency, then we replaced still JPEGs with the superior HEVC/VP8 intra-frame compression formats (i.e. HEIF/WebP), only to replace that with JPEG-XL (hopefully soon) – which is apparently a good starting point for a simple animated graphics codec :)
The intended replacement for animated GIFs was MNG, but it never took off.
There's a lot of use cases, and the irregular development of the different technologies has lead to ebb and flow between different methods. But it's not going in a circle. If you track specific use cases, you'll see them moving a lot less.
it really is a different thing, because it supports progressive loading (you get lo-res animation initially, and then load up more details just like with non-animated progressive image)
(unless this feature got trashed during the multi year finalisation. best technical discussion about it still seems old FLIF/FUIF posts and encode.su threads)