Re: There is no direct or indirect connection between the configuration settings of your two different devices
Yes, correct, AquaMail on each device is fully independent of AquaMail on other devices.
That being said, what are your accounts on the app's main screen (account list) and how are they set up?
A Gmail account added as "Gmail / Google Apps" will show in system accounts as "AquaMail (Gmail)", this uses Google's preferred OAUTH to log in.
A Gmail (or any other) account added as "Internet Mail" (which then gives you the choice of IMAP or POP3) will show in system accounts as "AquaMail (Internet Mail)", and does not use OAUTH.