I would think it's just the company name - "Advantage Notary." I don't believe notaries bond anyone in the U.S, so I'd guess that the company started as a notary service and expanded from there.
It's all just a guess, though.
A quick search for Advantage Notary of Florida turns this up:
Thank you for visiting Advantage Notary of Florida. As you may know, we have made some changes to our look and address.
As of January 1, 2004 1st State Insurance now maintains the Notary application processing as well as the Notary Bonding side of the operation.
I see what my confusion was. Notaries must be bonded, and apparently this company provides bonding for notaries, or did provide it at one time. As far as I know, notaries must be bonded by an insurance company in California. The law is generally much more lax about a lot of things in Florida.