The difference is once you got a Gmail account you could immediately start sending and receiving email from it rather than twiddling your thumbs till someone you know got invited.
This, and also that GMail solved a need you already knew you had, and could be explained in a few words: practically unlimited inbox space, no need to delete emails anymore! Everyone wanted that, but most people didn't know exactly why they should want Wave.
Gmail invites, by 2004 or 2005(?) when I got in were instant. If I sent the invite, the friend had a chance to sign up right then.
But email was already an existing protocol. So invites meant nothing. I could still communicate with my family even though they were still on their ISP account. Or my sister with her university account.