Hmmm, well let's see.
Technically:
The Construction Grid is set relative to Project Origin.
The Snap Grid is set relative to the User Origin or Edt Origin.
So if you're snapping to the Snap Grid, it will matter where your User Origin or Edt Origin currently is. If you're snapping to the Construction Grid it doesn't matter where your User Origin or Edt Origin currently is.
Furthermore if you have switched to the Rotated Grid, then the Construction Grid will no longer be relative to the Project Origin, but relative to the point at which the rotation was first established, and it will be aligned with the angle of the Rotated Grid
More importantly, the Snap Grid will still be relative to the User Origin or Edt Origin, but will be aligned with the angle of the Rotated Grid.
Assuming your User Origin is back at the Project Origin, it's possible that you may have your Grid switched to Rotated Grid even though the rotated grid may not be rotated at all, whilst snapping to the Snap Grid. If so, switch back to the Orthogonal Grid as per the image.
Or your Origin is not at the Project Origin and you're snapping to the Snap Grid. If so, reset your User Origin back to the Project Origin.
Cheers,
Link.