Yes, unless you are on PC and use some mod that changes this, it is always Morndas, 17 Last Seed, 4E 201.
It may be a glitch, but sometimes I start on Tirdas, 17 Last Seed, 4E 201. (I'm on Xbox)
The day of the week is probably the only difference between games. The day number, month, and year seem to always be the same.
For me it's either Morndas or Tirdas.
It got horribly confusing when I tried synchronizing several RP save files and some characters were a weekday ahead even though the day of the month was the same.
My main character's birthday is the 30th of Sun's Dusk.