Free vs available disk space huge difference, what is going on?

The "available" storage is the amount of used storage that the operating system could automatically delete if it felt that it was really necessary. The "free" storage is the amount that you can actually use for something.

There are system processes that run in the background and automatically delete some of the "available" storage and convert it to "free". If you completely run out of storage, then those system processes will try a little harder. When you "delete" files you are just hinting to the operating system that you don't need those files anymore. The operating system will eventually remove them, but on its own schedule.

Certain tools will allow you to force the issue and manually clean up some of this storage and manually delete local snapshots. But that is only temporary.