Recording iPhone screen (iOS 11.4) using QuickTime on macOS 10.13.4
The option you are looking for is New Movie Recording.



To record iPhone screen:


Select New Movie Recording.
Click on the dropdown besides the red circular record button.
Select iPhone under Camera (and Microphone if required).
Hit the record button.
Voila! you are recording your iPhone's screen now!
Once done, hit stop and save the recording at the desired location on your Mac. Note that the recording is saved on disk on Mac and not in the iPhone.