Do Americans refer to those constrictions as Improved Cylinder and Modified?
Yes. But, there is significant variance. A 12 gauge I/C could have as little as .006” to .011”. Mod could vary from about .017” to .023”.
But what matters is performance. An I/C should throw 50% of its payload into a 30” circle at 40 yards; a modified, 60%. Performance is the key measure of choke, not constriction. To further muddy the water, performance varies considerably with ammunition used. For example, an old trick for “opening“ a choke is to use cheap promotion ammo, or higher quality ammo to tighten a pattern.
