How to completely turn off cellular on iPhone?

I normally reside in the USA but am in Korea this week. To avoid high cellular charges from my domestic provider, I want to completely turn off all cellular services on my iPhone for a few days (I can easily live on wifi only for the next few days).

Per the image below, in Settings > Cellular, I have turned off everything that has an On / Off button. Also, when I swipe up form the Home screen, I have tapped the cellular icon to turn it off. So I think, but am not sure, that I have turned off all cellular.

But two things still puzzle me. First, my iPhone still auto-connects to a Korean cellular provider, which I see in the upper-most status bar on the home screen. And second., I have received (but not answered) two calls from Korean phone numbers. So if I have cellular fully turned off, how is it that a) my iPhone still connects to a cellular provider, and b) that I still receive phone calls?

Is there something else I need to do, short of removing the SIM card, to fully turn off all cellular services? Thx