Autoattack Animations

When I played AD Annie just for fun with my friends, I noticed that she seemed to to less damage than someone like Nocturne with the same attack speed items.

Do autoattack animations affect attack speed in any way? If the entire attack animation is counted as one auto attack, then Annie would do less damage because her fireballs travel so slow. If it doesn't, then could there be multiple fireballs flying through the air?

Also, I believe melee attackers like Nocturne have faster attack animations than ranged attackers like Vayne. Is this true? Who has the fastest and the slowest attack animation?