If you logged in to a different account by accident, you can use the "Log Out" button to sign out of said account. Go to your Settings menu (Mailbox > Settings tab) and on the right side of this window, tap the red "Log Out" button. This will log you out of the account you were playing on currently and bring you to the title screen. On the title screen, you can select any other account you wish to sign in with: Guest, Platform (Apple/Google), or Facebook.

Please keep in mind that once a Apple, Google, or Facebook account is signed into, it will remain in the title screen for easy access and cannot be removed. If you wish to log in using different Apple, Google, or Facebook credentials, please clear the app's cache and/or uninstall and sign in with the desired credentials.