The basics are pretty much the same today as a hundred years ago. There's only so many ways to do the standard sewing machine stitch, one really, but newer machines may be able to do different stitches. You may have needed a different machine set up for the different stitch, before.

There have been many sewing machine companies, and you're very correct in that Singer is probably the most well known. They've simply produced a good product, and were literally the first to hit the market. They've managed to maintain popularity and good products since their founding. Other companies definitely exist, though. Companies like Brother have developed features that make sewing at home much easier, and Juki is actually the king of sewing machines worldwide. My parents have a Juki from the 80s which is still running strong, and still worth a few hundred bucks.