The California poppy is a annual poppy.
I have grown the Iceland poppy from seeds before.
The icelands bloomed for me one year and never returned.
The iceland poppies can behave more like a annual or biannual poppy at times.
You can sow both types of these poppy seeds in the late fall.
Here is the way I look at poppies. I just love the flowers. But the oriental poppies flower for a week and then they are done. Not good enough. Ok, so I am not going to throw out the one I have but I am not going to buy another either. I need more bloom.
I did buy some spring blooming poppy plants that never came back or reseeded one year, I bet they were Iceland poppies. (Or maybe Shirley poppies).
I don't like the folliage (too coarse) on the breadseed poppies.
I need to do more reserch and ask more questions still yet. I just got serious about this this spring lately.
Another difference is that Calfornia poppies are a lot more heat tolerant, not that they are super-duper heat tolerant, but they don't die out (for me) like the Icelandic poppies. Here, CA poppies are short-lived perennials and they self-sow like there's no tomorrow.