Where are SQL server Usernames and Passwords Stored in the SQL server?

There are two authentications

1. Windows authetication

The credentials for which are not stored in SQl Server database and managed by windows/AD. There would be entry for windows autheticated logins in master database with respective SID but password would be with Active directory.

2. SQL Server authetication.

For 2nd we have password stored in hash format you can see it from sys.sql_logins. The information about SQl server logins are stored in master database and each login has SID repective to it. Only SA login has same SID no matter what server it is. That is why when you move database by backup restore mechanism users are moved not logins and you finally have to create logins(if already not there) and map it to users. This is generally called as troubleshooting orpahned users

You can use sys.syslogins and sys.server_principal to gain more information about logins. Note that sys.syslogins is a legacy view.