It depends on what phone and Android version you have. Different versions handle some things differently, and some manufacturers make their own changes
On my Pixel 2 (currently android 9 but it was the same on 8) I can go into Settings, Sounds, Advanced, Do Not Disturb and then select Calls (which appears under "exceptions"). There's an option there for who I allow calls from, and "starred contacts" is one of the choices. There's a similar setting for messages.
If that doesn't help you find it, tell us what phone you have and hopefully someone will be able to tell you where to look.
Of course that's for the "do not disturb" mode. If you manually set the phone to vibrate or something like that it will assume you know what you are doing and not override it (I would expect that your iPhone didn't override the "ringer off" switch on the side either - I'd have sent it back if it had).