Profiles are probably better explained in the scattered bits about how they are implemented in the file system. There is currently work in progress to unify that: https://github.com/NixOS/nix/pull/8141
Home-manager manages programs and their configuration.
When used standalone, then it will use nix-env or nix profile to actually create and maintain the information to nix which things are contained in the users “default” profile which gets linked through ~/.nix-profile.