That's a great explanation, I don't know why I didn't get any notifications for this!

A tiny correction is that the extruder is the motor that pushes the filament to the hotend and on this specific printer its actually seperate from this carriage and uses something called a bowden tube; think of it like bicycle cable brake lines, where the tube acts as the sheathing to push the filament through.

The whole X axis moving assembly is known as the carriage and on a lot of printers they're set up in a direct drive configuration which doesn't use bowden tubes and does actually include the extruder which is why a lot of the time it is referred to as that so I understand the slight confusion, I did it a lot when I got my first printer!

The carriage always includes what's called a hotend, which is the bit that melts the filament so you sometimes hear the carriage being referred to as that.