Here's one for the trivia enthusiasts. I used the two terms interchangeably until a few years ago, when I was politely corrected as I was calling around for parts to repair an old bench jigsaw. A jigsaw has one motor-powered arm to pull the blade down, and a spring-actuated opposite arm to pull it back with each stroke. A scroll saw has two parallel arms that both move in unison under motor power. I'm told the scroll saw gives a smoother cut because tension on the blade is more consistent. I think both would be fine for roughing out rings in your application.