I think it was just marketing. The Singers used to cost a lot compared to the typical family's income. The 503 is a stripped-down version of the 500, and you can incrementally upgrade it to the same capabilities by buying cams. So, I think "Special" was just marketing spin to make a less-featured machine sound more attractive.
Kind of like Ford used to sell a very plain stripped down pickup as the "Custom." Sounds better than "De-contented." Or "Economy Model." lol