Jeff, I believe these came from the same coin. As a metalworker, I can say this was likely done with a jeweler's saw, similar to a coping saw in woodworking. You can cut out pierced designs by drilling a small hole in the coin and threading the saw blade through the hole. This is very similar to how a scroll saw is used to make pierced filigree cut outs in wood. I can see the a clear saw mark on the bottom left corner of the dime. You can see where they cut a little too far past the bust.
One does not need a laser or water jet to cut metal. Humans have been cutting metals for 1000s of years before these things were invented.