So, that kinda explains what FIDs are, and starts to explain what a playlist is. I'll state it more explicitly here:

A playlist is simply a list of FIDs. It is stored in a *0 file on the player. Each of those FIDs can be another playlist or a tune.

Onto the next concept:

In memory, the player has what are called the "programme" and the "running order".

When you select a playlist from the menu, the player builds a new programme containing all of the FIDs from that playlist and its children. That's to say, at each step, if a FID refers to a playlist, it grabs the FIDs contained therein, instead. This process is recursive, and it's called "flattening". This results in a list containing the tunes which are descendents of the playlist you chose from the menu. Obviously, if you've got any special playlist attributes turned on (e.g. "ignore as child" or "select percentage" or whatever), this mechanism is changed.

This list of FIDs is stored in the player as the programme.

The running order controls the order in which the items in the programme will be played.

When you turn on/off the shuffle option, it changes the running order, but doesn't change the programme. If you select one of the tweak options, the player simply searches through the running order until it finds a match, and then swaps the order of the entries in the running order.

None of this makes it back to the playlist stored on the disk.