Both of the WAMU institutions are owned by the holding company Washington Mutual, Inc. The same website is used for all (www.wamu.com). This is normal that the holding company has the website and you access their institutions from the same site.
http://www.ots.treas.gov/?p=InstitutionSearch
What used to irritate me so bad when I worked for the federal regulator of national banks is that it appears some banks try real hard to make specific information like this not too obvious. The different addresses are just processing offices. As a matter of fact, the full name of the bank should be on your Cardholder Agreement but most people probably don't read those very closely or keep them handy.
I'm curious now & have sent them an email asking which institution issues their credit cards. Will let you know if I get a response.
Providian used to be a national bank and 'in my opinion' was using terrible deceptive practices in issuing some of their credit card accounts. They were finally fined and later closed and the accounts sold.