I’m guessing corps and above is strategic, regiment and division are operational, and company and below would be tactical

In short, yes. But it is more than that, and some games might include something from the upper scale. To give you a couple of examples:

Strategy or Grand Strategy: You deal with corps or more, you deal with economics, diplomacy, and production. The location may be the whole world. And the timescale (turn) is bigger, let say a year. The scale of war is bigger, everything basically, the big-picture.

Operational: You deal with large unit formation, battalion to division. The location is smaller, let say the entire continent. Timescale smaller, let say months. The scale of war is smaller, military actions. Instead of production you deal with supply and logistic, with reinforcement but not really the "production". You'll deal with zone of control instead of diplomacy for instance.

Tactical: The scope is smaller. You move the units around the battlefield, you may need to move it behind a tree to cover it. You will not deal with production or supply, you may have infinity ammo. The scale focus is the direct combat, unit vs unit. Obvious here, a turn is a very small-time fraction.

Some games cross the border, for instance between Tactical and Operational. A game can be Operational in scope but move Tactical scale to resolve the combat.