Phil,
It looks like you have an older, but very nice Star Universal machine in 38 Special. By changing shell plates and dies, a "Universal" machine can load and handgun caliber. Star also made a "Progressive" reloader which looks very similar, but was designed to load 38 Special only.
The shell plate on Star reloaders are advanced manually. With the addition of a case Feeder (which I don't see in the pictures) you can probably load around 400 rounds per hour, so manual advancement of the shell plate is not a big issue. However, there are after market indexers available, and many on this forum swear by them. Do a search for Moon Indexer on this forum and you will find several threads discussing them.
The Star dies have a 11/16-24 thread which is unique to Star (so far as I know) it is not the same as the Lyman 310 dies.
From the pictures, is looks like your sizing die might be steel rather than carbide. If that's the case you should probably keep an eye out for a Lifetyme or RLS Precision carbide sizing. It shouldn't be too difficult to find one in 38 Special.