Sorry, examples of what? Package managers that present themselves as replacements for other package managers? Or package managers that aren't compatible with the registry they're supposed to be compatible with? Your use of scare quotes is confusing.
replypnmp, npm, yard all have different lockfiles, all use the same registry format (and the same registry itself), all try to stay compatible in other ways.
replyYou won't be having situation where one uses yarn and someone uses pnpm on the same project tho.