It’s hard to see much in those pictures but is it possible the red one has rotted through? Is it squashy?

btw, I’m sure you know the bright colours are achieved by dying and new growth will be green.

If the top one is in its original pot, could you pls show a clear pic of its label?

Looks like they are in original peaty soil. They should be repotted using well draining mix. Get them out of pots and get all old soil off the roots. That will give you chance to inspect roots, if any. If roots are dead, try to re-root them. Any damaged roots - dry, broken and/or rotting should be cut off. If not sure, take clear photo of plants roots and post.

I can’t tell if the red one rotted and that’s why it broke away from the roots, or did something happen like a fall that made it break.

Regardless I would cut it around here.

The flesh in the cactus should be clean no brown spots. If there is brown areas keep cutting till the cactus flesh is clean.

Let the cactus cutting callus over for a week somewhere out of direct sun. Then pot up in a fast draining mix amended with half perlite or pumice. Keep the rootless cutting in bright filtered light. No direct sun till roots form because it could burn, and no water till roots form.

The green one you can pot up in the mix I recommended, but clean all the old soil off the roots. Water a week after repotting.

This cactus is Mammillaria vetula subs. gracilis cv. Arizona Snowcap that has been painted. The new spines will be white.

I have found this cactus to be a slow grower.

You can easilly root any of the branches that fall off or break some more off to root into new plants. They fall off the main plant very easily if you handle them slightly roughly.