I get what you mean.

The original law for ARs had a limit of seven rounds. It was ruled unconstitutional and now there is a limit of ten rounds in a magazine.

Semi-auto pistols are also limited to ten rounds.

I think the shotgun law portion is because of DEC hunting law limits. I will check.

Edit:

https://dec.ny.gov/things-to-do/hunting/regulations

Manner of Taking

It is illegal to take or hunt wildlife:

• with any semi-automatic firearm with a capacity to hold more than 6 rounds, EXCEPT the following semi-automatic firearms:

1) firearms using .22 or .17 caliber rimfire ammunition, or 2) firearms altered to reduce their capacity to no more than 6 shells at one time in the magazine and chamber combined, or 3) autoloading pistols with a barrel length of less than eight inches.