It's funny, I can't recall every hearing anybody say "satellite dish" for a terrestrial antenna in my years in metro and suburban California. I've heard "reflector dish", "dish antenna", "microwave dish", or "directional antenna" (which could also apply to YAGI and other non-dish structures).
I wonder if it is regional or has other socioeconomic factors? Actual satellite dishes weren't common structures when I was growing up, outside either a sports bar with satellite TV feeds or more commonly large dishes on industrial, military, or scientific facilities. Other, smaller directional antenna were more commonly seen on radio towers etc.