I remember back in January 2008 being under a Snow Advisory (first time I had ever heard of this) and being somewhat confused what the criteria was. Was it similar to a Winter Weather Advisory for us? I assumed it was because we only picked up like 1-2 inches from that storm at that time.
Most likely because of a small snowfall total. Before the switch of advisories, there was a Heavy Snow Advisory, which was likely for larger snow accumulations.
Today, a Winter Weather Advisory just means winter weather conditions, whether it be icing, snow, or freezing rain, meet advisory criteria, but not warning criteria. So, you could have had an Icing Warning back then and today's Winter Weather Advisory could mean the same thing. They merged a ton of things into that single product.