I'm not understanding the difference between the criteria to determine if an inoperative piece of equipment should prevent you from flying the plane.
leaving the battles of the superpilots who look down their noses at those who don't mind a little safety enhancement...
Joe, as others said, they are telling you to look at different things. Without getting too technical,
Is this equipment required by the VFR-day type certificate requirements?
(FAR 91.213(d)(2)(i))
When you hear "type-certificate requirements" think "the aircraft rules that were in effect when the airplane was approved for manufacture." In most cases, that information will be reflected in the TCDS, which are available online.
Is this equipment required by the aircraft's equipment list or the kinds of operations equipment list?
(FAR 91.213(d)(2)(ii))
When you see this one, think of two places in the modern POH (there will be an equivaent for older airplanes, but you may have to look harder). The two places are in
Section 2, Limitations and
Section 6, Weight & Balance/Equipment List. Section 2 may have a subcategory for "kinds of Operations Limits" that may not have much, but will often direct you where else to look. The Section 6 Equipment list is usually have a key about what equipment is required and what equipment is not.
Is this equipment required by 91.205, 91.215, 91.207...?
(FAR 91.213(d)(2)(iii))
IMO, this is the biggest problem of the bunch because it's the one that is often taught through the use of some idiotic mnemonic making it seem that it's the only important one. It may even be the source of your thinking that they are redundant. But they are not. These Part 91 regs tell you bare minimums that apply to all aircraft, but the others tell you what applies, in addition, to
your aircraft.
There is going to be some overlap, but not complete redundancy. You can expect that a piece of equipment that is required by certification rules or regulation is not listed as "Required" in the Section 6 Equipment List (or equivalent), but it could happen if a Part 91 operational requirement changed after manufacture. For example, despite the requirement for anti-collision lights in 91.205 and 91.209. older aircraft equipment lists might still list them as "optional".
Or, there will be things in the equipment list that you won't find in any part 91 reg. I just pulled a 1976 Cessna 182 PIM off the shelf and it lists an adjustable pilot seat as "Required." Find that one in those Part 91 regs!