The girl is sitting next to a table.
girl waiting for friend
The girl could be sitting next to a table for any reason, it is not implied that she is waiting for a friend.
exists e1 x1 x2.(n_girl(x1) & to(e1,x2) & n_table(x2) & r_next(e1) & Actor(e1,x1) & v_sit(e1))
exists e1 x1 x2.(for(e1,x2) & n_friend(x2) & Actor(e1,x1) & v_wait(e1) & n_girl(x1))