Basically, when you are growing organs or organoids (or 3d printing organs) with stem cells (which are used for organ on a chip too), you're actually trying to recreate the physical organ itself in it's original structure/function. You can imagine in the extreme the end result of trying to do this with a lung would be actually having a working lung that you could transplant into a person.

Organ on a chip is less about making a lung, amd more about making a very controllable device that that has all the relevant behaviors and characteristics of a lung, so you can experiment with it. The end result of this might be a bunch of chips all connected to eachother with all sorts of tubes, and different cells grown in each tube with exact stimuli of all sorts being applied by an automated system. The goal wouldn't be to make a long you could put into a person. Rather, the goal would be to make something that, when you put a drug in through one of the tubes, would tell you exactly what would happen to the drug and how the lung of a real person would react if you were to give them the drug.

The lines can get blurred, organoids on a chip, 3d printed organs used for research purposes, etc. But in general, (and you'll see this in how the different companies market themselves) growing organs is trying to get functional organs that could eliminate the need for a donor for an organ transplant, and organ on a chip is trying to get perfect research tools to eliminate the need for mice in research.