Lgy_ in Dynare 4


I have some doubts switching from Dynare 3 to Dynare 4.
In Dynare 3, after running stoch_simul, the coefficients of the decision rules are stored in the global structure dr_.
Variables are re-ordered. The new order of variables is reported in dr_.order var, while variables in alphabetic order are listed in lgy_
Now in Dynare 4 I see that lgy_ is no more in the workspace. The order of variables in the decision rules is stored in oo_.dr.order_var. What does now replace lgy_? I see that there is the global structure M_. reporting the list of endogenous variables (not in alphabetic order). Is M_.endo_name replacing lgy_? Nevertheless, if it does, the order is not the same followed by Dynare 3.
Moreover, which is the difference between oo_.dr.order_var and oo_.dr.inv_order_var?
Thank you!