Semver is used for regular releases when you need to communicate deeper information to multiple consumers. A library version usually needs to communicate lots of information, to developers, to users, to distributions. Maybe this release is a dev release, while this other is stable, this release is LTS while another is not, this release has breaking changes, this one doesn't, etc.

Calver is used when you don't care about anything but the temporal difference between releases, and you can basically toss any expectation of compatibility between versions, other than something temporal ("this version is compatible with previous versions for up to one year"). That's why APIs use it.

Generally speaking, OSS uses Calver when the releaser doesn't need to care about the consumer, compatibility, etc. You'll find Linux system packages using Calver when someone basically cloned a random Git repo, made a one-off build, and decided "this will be a release" (you find this with firmware a lot), or as a way for 3rd parties to fork an official version with patches.

Random assortment of Ubuntu packages with a variant of Calver (sometimes along with Semver): libargon2, gyp, aspell, language-pack-en, libcrystalhd3, ntfs-3g, x11proto-* , python-cliapp, net-tools, rtmpdump, iputils-*, dh-python, amd64-microcode, lsb-release, libstring-escape-perl, wireless-regdb, ubuntu-keyring, tzdata, fonts-vlgothic, usb-modeswitch-data, publicsuffix, autotools-dev, geoip-database, ca-certificates, dns-root-data