Elite status is a carry over from STW. In the game files it's known as "Samurai" and can be set to either true or false. Units that are elite are not at all affected by routing none elite units ("ignores routers that aren't elite"). This is vital as it means that your CMAA or Knights don't take a morale hit once the peasants start running. This is a separate parameter to discipline.

Discipline is not the same as elite status. AFAIK none elite disciplined units can still waver when other none elite, none disciplined units rout, but are less likely to do so. I have observed this with Nubian Spearmen and others such as Byzantine Infantry on many occasions. Discpline comes in three types "Disciplined", "Normal" and "Uncontrolled". Discplined units are better able to resist the affects of routing friends and the generals death. Normal units are at the base level. Uncontrolled are the least disciplined, but they get bonuses from charging without orders.

This post by Puzz3D might be informative: https://forums.totalwar.org/vb/showt...ht=disciplined