They are synonims but "drug" is not so common anymore. So, "drug" means "friend" and also "drug" was used in comunism for members of Communist party or for teachers. "Prijatelj" is exactly like in English "friend". I haven't heard word "drug" long ago. If you use "drug" you won't have any problem, but it is beter to use "prijatelj".

Drug is simple a man who you consider as you friend. You can consider him as ¨drug - friend¨ even after a few days, but not as "prijatelj" because "prijatelj" is very close friend, almost your best friend. In Bosnia they would say "jaran" for "prijatelj" In Croatia, instead of "drug" they sometimes say "frend" female friend is drugarica, prijateljica - very close female, jaran - in Bosnian and frendica - in Croatian I hope this helps. If you have any questions, feel free to ask me.