The cookie that stores your PSN logged-in state persists even after logging out of Bungie.net. You can solve this issue by either:
A. Clearing your browser cookies
or
B. Going to the playstation website and directly signing out of your PSN account, therefore removing the cookie
After doing one of these, you should now be able to sign in to Bungie.net with a different PSN account.
Also, this belongs in #help
English
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Thanks for your help, first post on these forums so didn't know I had to use #help Clearing cookies seems to have done the trick, switching accounts on the playstation website worked on other websites except bungie.net, bit weird but atleast it works.