I think I was thinking of iChat. If someone started a conversation with you while it was in the background, it would display a small pop-up window in the corner of your screen, which you could click to start the chat. It appears in a screenshot here (from 2002): https://arstechnica.com/gadgets/2002/09/macosx-10-2/12/

So the basic design of the notification UI (small pop-up window, short and long, icon on the left, click to respond) was already in iChat. Other chat clients for Mac (Adium, Colloquy) were trying to imitate it, as I recall (and ended up improving on it).

This is also interesting on Growl's early history: https://web.archive.org/web/20060115015145/http://www.drunke...