Popup or prompt are functionally the same in my mind tbf ðŸ˜‹ I just think a lot of people have negative connotations associated with the word 'popup', if they're old enough to have been around in the 90s/00s online, or noticed the GDPR popups on websites in later years.
I think a good portion of people who argue against the idea of popups isn't necessarily because they disagree with its purpose, but its intrusiveness. Or perceived intrusiveness. So just the word immediately instills like an irrational "mental lock". But instead having a gameplay mechanic that prompts the player with stuff to do, sounds far more edible and evades that immediate impression of something being intrusive and disrupting their game.