You are exactly right, Rachel, your floors are shellac. My personal feeling is that shellac is one of the most underused and misunderstood finishing products. There are some packaging and handling problems associated with it, i.e. it has a limited shelf life but is excellent in many ways. It is also a very safe product and, at a high purity level, is used for coating pills.
Varnish is one of three different kinds of chemicals or a mixture of them that form real long molecules out of short molecules. If you are interested in a little longer but still readable explaination, check Bob Flexnor's book Understanding Wood Finishing. It is geared toward furniture but just as applicable to wood floors. And it has a lot of info on shellac too.
I wish that there was a simple answer to which one was better. The varnishes of today are a lot better than they were 20-30 years ago. Personally, I like Parks Pro Finisher Oil Modified Polyurethane but I don't think that I would be afraid of putting down shellac either. You might check out www.zinsser.com for more on shellac since they are the experts on this.