'while' is often used when the action is taking place at the same time as the person ex. "Okay, you wash the dishes while I clean the house." Unless past terms were used "She looked back while he walked away." "Meanwhile" can also be a present term where an action is done but may not be at the same place as the other one "The neverland kids tucked themselves to sleep, meanwhile Wendy stayed up with her thoughts of Peter Pan."