There is also an improved skeet choke, but I've never heard of improved cylinder skeet choke either.
For what it's worth, when you see "improved" in front of a choke designation, it generally means it is somewhat tighter than the regular choke by that name, but not quite as tight as the next regular choke designation.
I've never heard of an "improved skeet" choke either, but the name does make some sense. The name implies a constriction that falls between Skeet and IC. Seminole makes a choke like that, with a constriction of .008 compared with Skt at .005 and IC at .010 (in 12 gauge, that is - constrictions would be less in small gauges). I think it is unfortunate that Seminole has chosen to call theirs "Skeet II", which is a name used in the past for a choke that falls between IC and Mod - the same thing that is now called LtMod. It would make more sense for Seminole to call it "Improved Skeet" rather than "Skeet II". Perhaps some other maker does use the IS designation for what Seminole calls SktII, I'm just not familiar with it.
I doubt that you can find much difference in the patterns when you use open chokes that differ by 2 or 3 /1000". Hastings makes chokes that differ by 4/1000". My initial thoughts are that if you are worring about this level of choke difference you may not be paying enough attention to somethig else that may make a difference.
It takes a lot of patterning on paper to show the performance of chokes and loads. I am not ready to add to that for such a minor change.
Remington makes a Rem Choke that they call "Improved Skeet." The constriction on the one that I have (20 gauge) is exactly the same as the Improved Cylinder tube. The "Skeet" tube, on the other hand, has a negative constriction.
You won't know how it shoots until you try it, but it should be about like an improved cylinder choke. A true cylinder (or Remington "Skeet") tube might be more accurate, but shoot it first to see if it is acceptable.
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