If we simply look at how a trumpet works:
we need something to get the trumpet resonating. This sets up a standing wave in the instrument that sympathetically keeps the lips opening and closing like a switch at a specific frequency. Without an initial lip vibration accompanied by additional airflow, the horn cannot begin or continue to resonate. Period. The lips more or less float on air once the horn is resonating. When we use too much pressure, we squeeze off the lips and make that sympathetic vibration much tougher to keep going.
If some want to call this initial vibration that kickstarts the standing wave in the horn BUZZING, they are in line with at least part of what is generally understood. The problem is that once the horn is resonating, it takes the lips with it until we increase tension/air pressure to "buzz" higher.
We should not confuse the act of buzzing without a horn/mouthpiece with the kickstart that I just described. When I buzz a tune on my lips, there is no resonance to aid pitch production. The entire effort is in my face!
Maybe the word buzz includes too much information for some players. I use it freely in both contexts - with additional words to make sure that there is no doubt. A big IQ is not required to communicate. Freedom from agenda does help some though.