There were MIDP profiles[1] as long the version matched, the apps worked fine in my experience on any device although the devices themselves varied in their key pad placements; Nokia went crazy in their phone designs[2]!
I had a 3660 (friends called it the "communications brick"). There was no wifi and I couldn't afford a data plan but I was able to have the phone dialup via Bluetooth (think "reverse tether") to my Linux desktop. I never got into J2ME: being a fledgling Linux snob in college, I went for Nokia's C++ target and got stuck in the quagmire.
But MIDP profiles were so limited that you could only build the simplest apps. To do anything complex required calling proprietary extensions, which destroyed portability.
[1]https://en.wikipedia.org/wiki/Mobile_Information_Device_Prof...
[2]https://www.youtube.com/watch?v=YOZi-7V11k8