Technically no, effectively yes.
You can install and use different package managers on different distros, but with the exception of things like cargo it's highly recommended to not, as you are likely going to break your system.
[0] There are more of course, but those are the big two.
[1] I'm really only familiar with the Debian/Ubuntu space (Deb)
[2] See flatpak, snap, and nix/guix. Also some distros like Bedrock Linux let you have completely foreign environments mixing together.
You have 3 main "base" distros/package mamagers:
Debian/apt
RHEL/yum/dnf
Arch/pacman/pkgbuild
There are of course many more but these are the overwhelming majority.
This means if I wanted to make my own distro I could do as little as take Debian stable as my upstream, rebuild a few packages with a s/Debian/MyDisro/g and change a few default packages and call it that.
Or I could track a mix of packages from Debian testing and stable.
Or I could decide I prefer to build everything my self but still use apt for my package manager.
This is of course turtles all the way down eg: Mint is based of Ubuntu which is based of Debian.
If you do "sudo apt update && sudo apt -y dist-upgrade" then it breaks Mint desktop menu. To fix it, you can install all updates with mintupdate, and then "sudo apt -y install mint-menu --reinstall"
In other words, nothing good comes from trying to install two different package managers on one system.