I'm not 100% positive, but now I believe they are the same.
My spouse was approved recently, and got two separate emails on different days (about a week in-between), one about Welcome Notice Sent and the other about Approval Notice Sent. So we thought we would receive two different notices. All we got, however, was Welcome Notice only.
But if you see
this USCIS page, it sounds to me Welcome Notice is indeed Approval Notice. Indeed, Welcome Notice says something to the effect that the notice was to notify the case was approved.
When I was approved early this year, I got Approval Notice only. So my guess is they may have changed notice names sometime during the last half year (and due to some system bug and the like, the "Approval Notice Sent" email is still being sent).