For whatever reason when I published my server for the first time to Azure some really long password was generated for me that for whatever reason I didn\'t think would be a
No it is not the same. Reason is pretty clear - security concern!
My "Azure Admin Password" is to manage all my Azure Resources. While when I publish a web site to Azure I would expect to have some other credentials, that do not have to all my azure services.
What you see there is a Deployment Credential. This is best explained in the Wiki Page for the Kudu Project. Note that Azure Web Sites run Kudu.