There seems to be a movement away from the levels because everyone seems to be at odds with the transition. Level 3, and Level 4 have transitions from the car driving to requiring the human driver.
The definition of level 4 does not require any hand off. It is just that the car can't operate in certain conditions (presumably it'll come to a safe stop if it detects such conditions during the course of travel). A Level 3 car is the one that requires hand off.
Where L5 doesn't have that messiness, and I view Full Self-Driving as L5 driving. You did leave off the FULL from the self-driving.
Even if you keep the "full" part, there is still a level of messiness because the SAE definition changes two parameters at once moving from L4 to L5 and is still a bit vague.
Level 4:
driving-mode performance vs Level 5:
full performance
Level 5: all roadway and environmental conditions that can be managed by a human driver
Driving mode is a type of driving scenario with characteristic dynamic driving task requirements (e.g., expressway merging, high speed cruising, low speed traffic jam, closed-campus operations, etc.).
http://www.sae.org/misc/pdfs/automated_driving.pdf
This makes in unclear in colloquial usage. Wired counts the google car as a "level 5", however, it doesn't meet the strict definition of the SAE article above (particularly it can't handle highway or bad weather conditions, although it tells you that it doesn't before it starts the journey and presumably it can come to a safe stop on the side of the road if conditions deteriorate).
Everyone Wants a Level 5 Self-Driving Car—Here’s What That Means
Here's another definition that says level 5 is a car that has
no option for human driving (no steering wheel or controls). Obviously the Model S won't meet that definition.
Autonomous driving levels 0 to 5: Understanding the differences - TechRepublic
Another interpretation can be level 5 is a car that can operate with no one inside (even if it doesn't meet all driving modes/weather conditions).
Basically, if a car was like the Google car (which requires no driver and even has no controls), but can't operate in certain driving modes (like on the highway) is it still "level 5"? Can it be considered "full self-driving"?
And if it can handle all driving modes, but not necessarily all weather conditions, is it still "level 5"? Can it be considered "full self-driving"?
What if it can handle all driving modes, all weather conditions, but there are still some exceptions where it doesn't operate like a human (like the policeman directing traffic example people like to bring up). Is it "level 5"? Is it "full self-driving"?
Under the current vague/contradictory definitions, it seems open to interpretation.
I'm not even sure if Elon said level 5 specifically or if reporters interpreted that full self-driving = level 5?