If $j : V \rightarrow M$ is an elementary embedding, what can we learn in $M$ from $j''ORD$?  That is, what is $M[j''ORD]$?  

In particular, 

<blockquote>Is it $M[j''ORD]$ equal to all of $V$?</blockquote>  

If not, do we get a model intermediate between $M$ and $V$?  If $\kappa$ is the critical point of $j$, is $\kappa$ still a large cardinal in $M[j''ORD]$?  I am thinking of $j$ arising from a measure on $\kappa$, but I'm also interested in the more general situation.

My thinking goes like this:  If we have the image of all of $V$, we can reconstruct $V$ itself by taking the Mostowski collapse of $j''V$  (and $j$ is the inverse of the Mostowski collapse).  In $M[j''ORD]$, let's consider the class $W$ of sets with rank in $j''ORD$.  Does the Mostowski collapse of $W$ yield all of $V$, and if not, what's missing?  

EDIT: formatting, clarification of question.