Two "t"s; it's named for colonial Governor Spottswood, "cleverly" transformed into Spottsylvania.
One of the absolutely idiotic features of the organization of Grant's army ( and an important reason why he HAD to be present with it ) was the position of our old friend, Ambrose Burnside: When Burnside ignominiously left the AOP in Jan., 1863, he took the IX Corps with him; subsequently he served as a department commander in Kentucky and Tenn., but at the same time retained the corps except for its temporary service under Ord at Vicksburg where it served facing Joe Johnston in the rear of the siege lines. After Burnside's successful defense of Knoxville from Longstreet during the Chattanooga Campaign, again commanding the IX Corps, his star had regained much of the luster it had lost at Fredericksburg and in the Mud March.
When Grant brought Burnside and the IX Corps back to Virginia for the Overland Campaign, naturally Burn refused to take orders from Meade, who had only been a brigadier commanding a division under him at Fredericksburg! The answer to this dilemma: Burnside and his corps were NOT considered part of the AOP, so Burnside wouldn't have to take orders from his former subordinate. That meant Grant had to issue entirely separate orders for the movement of the IX Corps, a significant reason it often acted out-of-concert with the rest of the army, like in its moves in the Wilderness, where it essentially got "lost" right in the middle of the battlefield!
WHY did Grant ( or Lincoln, for that matter ) put up with this ridiculous situation? POLITICS, of course! Burnside was from Rhode Island, and was for some reason considered important to the New England war effort. Besides, he was considered a likeable ( if dull-witted ) guy, whose heart was in the right place, even if his head wasn't. Henry Halleck could have just as easily pulled the same stunt, refusing to serve under his former subordinate, Grant, but fortunately for the Union war effort, unlike Burnside he rose above the situation.