Looking on the internet deeply has found these results:

on the same date is the most popular phrase on the web.

on the same day 1140,000,000 results on the web	on the same date 13,330,000,000 results on the web More popular!
Some examples and use cases from the internet:	Some examples and use cases from the internet:
So we were at the mall on the same day. In fact negotiations were launched on the same day. The DOD meeting was on the same day as that horrible murder. So ?SA received notice of this assignment on the same day. And it turns out Ira bought a penthouse in Miami on the same day. you collared an international criminal and a wanted local on the same day. My life ended when she died, on the same day you were born.	So. Ge. A.AL submitted its observations on the same date. The two proposals are further explained in a communication adopted on the same date. Decree New hedges with a total nominal value of Euro 480 million, covering the period 2012 Every year on the same date. 10% discount for 3 or more students enrolling for a course starting on the same date... 2014, came into effect on the same date. law 54, adopted on the same date, sets out the new measures.

on the same day

1140,000,000 results on the web

on the same date

13,330,000,000 results on the web

More popular!

So. Ge. A.AL submitted its observations on the same date.
The two proposals are further explained in a communication adopted on the same date.
Decree
New hedges with a total nominal value of Euro 480 million, covering the period 2012
Every year on the same date.
10% discount for 3 or more students enrolling for a course starting on the same date...
2014, came into effect on the same date.
law 54, adopted on the same date, sets out the new measures.