Why does 'df' not show changes after running CleanMyMac? I've used CleanMyMac to remove around 40 Gb of files, but a before/after of df -h doesn't show much difference at all:

# Before:
[Kens-MacBook-Pro:~] % df -h
Filesystem      Size   Used  Avail Capacity iused               ifree %iused  Mounted on
/dev/disk1s1   466Gi  445Gi   18Gi    97% 2138098 9223372036852637709    0%   /
devfs          188Ki  188Ki    0Bi   100%     650                   0  100%   /dev
/dev/disk1s4   466Gi  2.0Gi   18Gi    11%       2 9223372036854775805    0%   /private/var/vm
map -hosts       0Bi    0Bi    0Bi   100%       0                   0  100%   /net
map auto_home    0Bi    0Bi    0Bi   100%       0                   0  100%   /home

# After:
[Kens-MacBook-Pro:~] % df -h
Filesystem      Size   Used  Avail Capacity iused               ifree %iused  Mounted on
/dev/disk1s1   466Gi  445Gi   18Gi    97% 1899364 9223372036852876443    0%   /
devfs          188Ki  188Ki    0Bi   100%     650                   0  100%   /dev
/dev/disk1s4   466Gi  2.0Gi   18Gi    11%       2 9223372036854775805    0%   /private/var/vm
map -hosts       0Bi    0Bi    0Bi   100%       0                   0  100%   /net
map auto_home    0Bi    0Bi    0Bi   100%       0                   0  100%   /home


In this case the removals were in two stages, first doing a "Smart Scan" that says "10.13 GB Unneeded junk removed", and then using Space Lens to manually select items, after which it says "CleanMyMac has freed up 30.21 GB of space on your Mac."
Taking @at0mic's comment as a starting point, I have a theory about what's happening:


Since the Time Machine snapshots aren't physical copies, they're still hanging on to the same inodes that CleanMyMac deleted.


Since the snapshots didn't take up more room when they were created (see https://www.zdnet.com/article/the-apple-file-systems-killer-feature-clones-and-snapshots/ - they just create one more reference to the same inodes), I also won't get back disk space right away when deleting stuff.

This makes sense to me.  However, when I went into Time Machine and performed "Delete all backups" on one of the large items I'd deleted, the disk usage as reported by df still didn't reduce.  So I kind of believe that Time Machine is the explanation, but there are still pieces I don't understand, so if I figure it out I'll edit this answer.