"auslachen" - to laugh at somebody (because they did or said something stupid) "anlachen" - is usually translated as "to smile at" because as far as I know there is no exact translation. It's what you do when you think somebody looks really nice and you'd like to get to know them better (not just in a man/woman-way!). Therefore, it's stronger than "to smile at", because you could smile at somebody thinly, or in a polite way, or just because it's what you do, right? It's not used so much anymore, but you could actually say "Ich habe mir bei italki mehrere interessante Sprachpartner angelacht" = I've found several interesting language partners here on italki (like: just by being friendly to them)

Viele Grüsse*

Hallo Skylar. Ich bin überhaupt nicht sicher, aber ich habe darüber eine kleine Idee: Mit AUSLACHEN lächt man über jemanden und mit ANLACHEN lächt man mit jemandem. Was denkst du? Kann das sein? Viele Grüssen!