Plywood thickness might depend on where you buy it, and how it's marked. Not all manufactures adhere or use a standard grading system. Domestically, plywood is generally graded into three groups. Decorative, construction, and shop.
The words "cabinet grade" are plywoods not graded by the HPVA. It is grading that uses an alpha character for both sides. It refers to plywood that could be suitable for building cabinets.
If you buy plywood that is marked "ANSI/HPVA", it has been marked as it applies to specific manufacturing standards. If domestic, it's likely ¾" thick, and likely you have face veneers .0625, or .040. The face veneer is marked with an alpha character A-C, and the back veneer is marked with a numerical character 1-4. Each of the grades has it's minimum standards for that grade. Decorative plywood is classified with this grading system.
Construction grades will have an alpha character for face values, and the backs can be numerical, or an "X" for "exterior".
Plywood marked otherwise is available for sale, and could have a variety of markings depending on the country of origin. Many just use an alpha character for both sides, but the overall grading may not comply with the standards set forth by the HPVA. That plywood generally falls into the "construction" category. The face veneers could look very nice, and be considered suitable for cabinetry, but there could be quality problems such as varying thickness, voids, odor, out of square, undersized (L-W).
Most plywood suppliers carry plywoods in varying species of face veneers that are referred to as "shop" grade. This plywood is accepted as being for whatever use you feel like using it for, but it's understood that it does not fall into the regular grading as "decorative" or "construction". These plywoods are like seconds, sold with the caveat that anomalies are present.
Plywood thickness should be checked.
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