Tactical, Operational, Strategic

I've seen a few posts about the differences between these terms. Often, I hear people saying "units are battalions, so it's not tactical" or "units are divisions, so it must be strategic". My thoughts are that the scales are differentiated by mechanics rather than the size of the units involved:

strategic: the game system involves both supply for maintaining units and production for building new units.
operational: the game system involves supply but not production. That is, the time scale is too brief for new units to be produced. You may be able to bring on re-inforcements, but you're not truly building new units.
tactical: Involves neither supply nor production. You may have ammunition limits and, again, you may have reinforcements, but at this level, the battle has been joined and fresh supply won't affect the unit's status until the battle is over.

I've also seen the terms "grand tactical" or occasionally "grand strategic". These are harder to define. To me, grand tactical is about an entire battle, whereas tactical is a section of that battle. So, for example, refighting "Gettysburg" is grand tactical, but refighting "Devil's Den", "Little Round Top", or "Pickett's Charge" (parts of the Gettysburg battle, for those of you not "into" the American Civil War) are tactical. Strategic vs. grand strategic is even less clear to me, but I would think both scales should involve production. Perhaps grand strategic might refer to all of World War II in Europe (or even all of WWII) whereas strategic might refer to an extended campaign such as the Eastern or Western fronts.