The question about WHAT AA-weapons were planned for the USS IOWA class (and other USN ships) was driven by the outbreak of war in Europe and the experience feedback from the UK to the USA. In the Spring of 1940, Adm. King initiated a board to study ANTI-AIRCRAFT DEFENSE IMPROVEMENTS TO THE FLEET. It was realized that the current "medium-AA weapon", the quad 1.1-in gun mount was inadequate. Several alternatives were studied, until the Swedish Bofors was considered to be a better option that "could" be produced in relatively short order. A sample "twin 40-mm" Bofors mount arrived in the USA in August 1940. Comparative testing took place and BuOrd was impressed with the guns performance, but soon realized that this weapon as it was produced in Sweden, had problems for mass production. Most of the components were "tailor" fitted for each gun. The USN preceded to redesign the guns for US production lines with interchangeable parts. This all took time and mounts produced in the USA and settling license agreements with Sweden, means that mounts weren't ready until early 1942. Even then they couldn't be installed until new fire control systems were also, developed and put into production. The first "production" twin 40-mm mounts were delivered in May 1942. The first shipboard mounts on "fighting" ships and not training ships, took place in about July 1942.
The King Board AA-Defense Improvement Plan came out in December 1940. The 40-mm guns were to be the ULTIMATE medium AA weapon, but quad 1.1-in mount was considered to be the best "INTERIM" option. Even then, production of the quad 1.1-in mounts lagged demand and single 3-in/50 guns were installed as a stop-gap weapon.
What this means is that depending on when given drawings of the new IOWA class were drawn, AND when the ships in that class were scheduled to be completed, the weapons in those plans that were to be installed could change. The first two IOWA's design in 1938 included quad 1.1-in and 50-cal MGs. However, they were laid down in 1940. This would mean that the "Build Plans" would have been altered with the previously planned quad 1.1-in mounts being replaced by 40-mm mounts and the 50-cal MGs replaced by 20-mm guns.
This is a VERY short summary of USN AA-weapons development from 1939 to 1942. Lots of reference material goes into the ugly details.