1. Yes, the COVID treatments we're using today are vaccines. The word has never meant Perfect Forever Invulnerability, we have a 200-year history of things labeled "vaccine" even when it didn't remove all symptoms, cover all strains, or need only one shot, etc.
2. No, the "normal" vaccines "back in your day" do have problems, and there are very good reasons we're pursuing new types like mRNA. For example, live-virus vaccines (containing a weak relative) can sometimes start their own spreading infection, and inactivatived-vaccines (with blended-up chunks of virus) require more doses and can sometimes mis-train your immune system.