The most obvious difference is that the M10 replaces the iconic Ercoupe-style dual vertical stabilizer with a tail designed to allow the airplane to spin.
Changes to the ailerons, along with replacement of the A2-A's tail, were motivated by Mooney's intent to market the M10 as a trainer: student pilots receiving training in a non-spinnable airplane, as the Ercoupe was, were issued FAA pilot certificates carrying the restriction that they could only fly airplanes which were "characteristically incapable of spinning"; thus the spinnable tail was necessary to turn the A2-A into a general-purpose trainer.
Given that they were replacing the tail, Mooney's engineers opted to give it the "backward" profile characteristic of the M20 series.
Although the M10's empennage has the same silhouette as the "big Mooneys", it does not swivel the way the M20's does; the Cadet's tail is a conventional design with fixed horizontal stabilizer, hinged elevator, and trim tabs.
The two type certificates that cover all Ercoupe variants, including the Mooney M10, are currently owned by Univair Aircraft Corporation, in Aurora, Colorado, USA.