The Florida notary commission number I had when I became a Florida notary previously is not the same as the notary commission number I received upon renewing my Florida notary commission. Shouldn't the numbers be the same?

Florida notary commission numbers are issued per notary commission, not per Florida notary. Therefore, each time you renew your term of office as a Florida Notary Public, you will be issued a new Florida notary commission number for that specific notary term. Once a Florida notary commission expires, so does that coinciding commission number.