Ok, OK, my bad. They are OLED displays. i.e. the devices that @maik_s showed previously.
But they work like hd44780 LCDs... 
So far I have the larger one up and running with the library supplied by joy-it
It is a pretty wimpy library and the API is not very compatible with the LiquidCrystal API or LCD API 1.0
joy-it product/datasheets for that larger display are here:
https://www.joy-it.net/files/files/Produkte/COM-OLED16x2/COM-OLED16x2-Datasheet_2021-03-11.pdf
https://www.joy-it.net/files/files/Produkte/COM-OLED16x2/COM-OLED16x2_Manual_2021-04-23.pdf
And their demo library is here:
The device comes strapped for 6800 mode but can strapped for 8080 mode or SPI.
I'm just about to get started on getting the hd44780 library to work with it.