As most have said, races are fairly specific to the headset. Some work with each other, some don't. Bearing angles, sealing, height, diameter etc all play a part. Like someone else mentioned, there are some headset races that fit a king. Iirc, I found a split allot one I had spare fitted like a glove. I also have been known to cut a slot in a king race to make it easier to fit and remove. As bearings are sealed it doesn't make a difference.
Tools are a good investment if you think you'll use them. I've certainly had my money's worth on a few headset related tools. Headset press, headset cup removal tool, crown race remover, star nut tool. I used to use a custom blade for race removal, always worked. I inherited it from my granddad's tool box, it was a bit of thin but strong steel files into a blade at one end. It could slot under a race and used to wriggle and lever the race off. I also used to use a wide ring spanner to get the race in place with the help of a few taps from a hammer. It was wide enough to miss the angled area of the race and sat on the flat part. Worked fine but I've graduated to the plastic pipe method if not using a split race.