In this explanation, keep in mind that g is not acceleration, it is load factor, n = lift/weight, in airplane coordinates. Let's go through a roll to the right at 90 deg/sec rate. The load factor, n, is constant at 1. Gravity is pulling down on the airplane. As the airplane rolls 90 deg, the lift is now horizontal in earth coordinates, so the airplane is accelerating to the right. Gravity is pulling the airplane down, so it is losing altitude, accelerating down in earth coordinates. Then roll to inverted, 180 deg bank angle. Lift is now down in earth coordinates and gravity is down, so the airplane is accelerating down at 2g, losing more altitude, but zero accel to the horizontal(earth). Then bank to 270 deg, and the lift is to the left (earth) with gravity still pulling down (earth). The airplane is moving to the left and still sinking. Then roll erect again back to wings level. The lift is now up and balances the down gravity, so you are back to level flight, but you have lost 128 feet of altitude. (Average down velocity is 32 ft/sec for 4 seconds).

So is that a barrel roll or an aileron roll? Looks like a sloppy barrel roll to me. Actually a crisply flown barrel roll is done in a shallow climb, so the loss of altitude is negated by the climb. Next time you see a roll at an airshow, chances are the airplane will enter a shallow climb just before the roll.

I assume you mean an "aileron roll" is a level flight roll, with no loss of altitude, like a zero radius barrel roll. To do that the g command must be modulated through the roll, 1g at initiation, 0g at 90 deg bank, -1g at 180 deg bank, back to 0g at 270 deg bank, and back to 1g at termination wings level. Practice that on your simulator sometime, not easy. The easiest way to do what looks like an aileron roll is to fly very fast and roll very fast, so the apparent loss of altitude is minimized.

I hope this is clear. If I screwed up somewhere, I'm sure someone will correct me.