410 not a Ga! I'm sure a few beer bets are going down on that one. I call them 410 Bore but most folks do call the 410 Ga. I guess Bore and Caliber are interchangeable terms.
Technically they are correct. Gauge, and Caliber are two specific and different methods for measuring a bore. Saying .410 bore is correct but very general, and a non-gun person would have no idea what you meant. If you told an engineer, scientist, or mathematician who knew nothing about guns that your bore was 410 gauge they would picture something that was small enough that it would take 410 lead balls the same diameter as the bore to equal 1LB, thus would imagine something much smaller than it actually is. If you told the same person .410 caliber, they would immediately know you meant 41/100 of an inch.