Yeah that’s the one! Only seen it once (coinciding with a supermoon which was frankly surreal).
Coronas are a bit different I believe, though another one of the same group. I’ve always just called them their individual names, with coronas being tighter and more spectrally-distorting than halos. Maybe the only other collective name I’ve heard would be the minimally descriptive “atmospheric phenomenon” but that’s no fun at all.
Edit: Just took a brief look and indeed coronas are related but formed by refraction through water droplets rather than ice crystals! Cool to know!