On vocabulary.com it reads that debut and premiere are not interchangeable:
A fun fact: debut and premiere are often thought to be interchangeable, but they’re not. A debut, as you now know, is a first public appearance. But a premiere, while also a “first,” isn't necessarily live. When a movie opens or an interview is broadcast for the first time, they're called premieres.
But I wonder how to check if the event is live or not.
In the entry of the premiere, an example is as the following:
It was quite a different sight a year later when Monteverdi’s new opera, Arianna, premiered. --The Story of Music
while in the debut page, you can find this example:
This young soprano debuts next month at the Metropolitan Opera
Does it also seem confusing to you?