Please do not change passwords for the time being as it sounds to me that you have 2 Apple accounts.
The first account is the principal one (the one you see in System Settings > [your name], right below your icon and name). This account is used for iCloud services such as synchronizing your data amongst your devices, or to access iCloud.com, or to access accounts.apple.com.
The second account is the one you use for your purchases. As I mentioned before, the purchasing account is usually the same as your principal account but it does not have to be this way. You can have a separate account for your purchases. To see this account, go to System Settings > [your name] > Media & Purchases and click the Manage button next to your name. If you see that the email address there is different than the email address you see for your principal account, you do have 2 Apple Accounts.
If you do indeed have 2 Apple Accounts, I would recommend that you transfer your purchases to your principal Apple Account (Migrate purchases from one Apple Account to another Apple Account - Apple Support) and that you drop the purchasing Apple Account to replace it with your principal Apple Account. This will you will have a unique Apple account where all the Apple services reside.
