Password-related oddities

Something very strange is going on with my account.
 
When I come to the Derpibooru site from Google, it tells me that I’m logged out and refuses to recognize my password when I try logging back in.
 
But when I use a link to make a new password and check in through my email, I find that I’m already logged in. Even though when I go to my account page and try using my current(?) password to set a new password for the account, it tells me that my password isn’t recognized.
 
What is going on and how can I get a new password for my account that will work?

Are you by any chance switching between *www.*derpibooru.org and derpibooru.org?

@Derpy Whooves  
When I come to the site from Google this is the address I arrive at:
 
https://www.derpibooru.org/session/new?request_path=%2Fnotifications
 
EDIT: Huh, I edited out the ‘www’ part and now it says I’m logged in!
 
I’d still like to get an e-mail telling me just what exactly my password is. I’m trying to figure out how I changed it.

Ah - yeah, we store separate cookies for each way of getting here. Makes it nice if you have two profiles - log into one profile on www.derpibooru.org, and a different profile on derpibooru.org, and you’re all set :)
 
As for what your password is, we have no way to see it. But you could send an email to ops@derpibooru.org and let them know that you’d like to reset your password, and they can help you.

@Ardashir  
Passwords are hashed using an extremely strong, computationally expensive one-way hashing algorithm. There’s absolutely no way to determine what your password is. You can request a password reset on the login form. Just make sure your email address is correct - I’ve seen a lot of people having login issues because there was a typo in their email address.

@Derpy Whooves  
Thank you.