I practice both @Dawn. I’m quicker in my moving, and more accurate when it’s move, then shoot. But, I do practice forward, and side to side while shooting. It’s something my ccw instructor had us do. It’s really nice to have a range buddy call out the target while you move, and the number of shots. Example=1 chest, 1 head 2 chest, 1 head.
We start at one end of either 3 or five targets, engaging until the pistol is empty, do a reload, and reverse direction. Make sure you use a lot of thinking, eye movements, and coordination. It’s fun too. Another drill, I do alone, is walk backwards engaging a single target until I need to reload, then advance on the target while emptying the firearm. I know, that me bing involved in a shooting is not likely. One of the things that concerns me, is while out for a walk, if my son gets ahead of me and my wife, either a child abduction(becoming less likely, as he’s as big as a small adult now) or being in the woods and a 4 legged predator attacking. I want to be able to quickly close the distance and start putting lead downrange, accurately, as fast as I can.