Cheap compressors are rated in SCFM which is as you state, input volume. I do believe industrial grade units rate CFM at a particular output pressure. Marketing eh?
CFM, SCFM, ACFM, all apply (according to what I've uncovered) to the air moved at ambient pressure. That goes for commercial and consumer units alike (again, according to what I've read). ACFM is SCFM corrected for ambient temperature, humidity, elevation, etc. And that's the source of the up-to-33% thumbrule I stated previously.
SCFM vs ACFM | Standard CFM vs Actual CFM
I started down this rabbit hole of "CFM of compressed air" vs "CFM of ambient pressure air" while investigating the use of large (10-20 ton) A/C scroll compressors as a source of compressed air. I was unable to find clearly defined CFM values for the vast lot of them, and it seems the reason is because they dont move [gas at ambient pressure] to [gas at a specific higher pressure]; they move [gas at a wildly variable "low" pressure] to [gas at relatively higher pressure]. So I deduced that they are not (typically) rated in CFM like an air compressor because there is no ambient pressure reference. My research seems to confirm that.
Evaluating True Horsepower and CFM Ratings of Air Compressors
When a compressor pumps one "CFM" (cubic foot per minute), that means the intake port inhales one cubic foot of "free air" (air at atmospheric pressure, which is 0 psig) per minute. (Note: A CFM does not mean in any sense the compressed volume.) So the unit really measures the mass of air flowing per minute, not volume per minute, since a cubic foot of free air is a unit of mass. Some people labor under a stubborn misundertanding that these units refer to the flow of compressed volume (as opposed to free air volume), but this is flatly wrong. The confusion arises because the term "cubic foot" sounds like a measure of volume, when in fact this term in this context is an abbreviation for "the mass of a cubic foot of atmospheric air", which is a measure of mass. This nomenclature dates back to the 19th-century era of steam power, which is still quaintly with us.
There usually is some difference between the ratings of anything consumer grade (almost assuredly skewed/inflated) and its industrial cousin. Industrial units are more often specified by Engineers who need factual data to ensure capacities in compliance with their design specifications. Consumers are usually after the bigger number for the smaller price and rarely verify the big numbers or make any kind of weighty stink when they dont add up. In this case, I think the MFGs of consumer grade products are (in contrast to commercial MFGs) guilty, not of failing to specify the capacity in terms of volume of delivery at system pressure (a difference of 1,000%+ from ambient), but of:
1. As you said, by listing their rating in SCFM rather than ACFM (a difference in my estimation somewhere between 5% and 30%)
2. Using the "@"/"at" term to imply that the capacity
is of volume of compressed air delivery. Which, in my opinion is an outright lie. I mean, we all know what the word "at" means, right? How is its use in that context to be interpreted as anything other than cubic feet per minute of air
at system pressure? But I'm sure that through some muddled abortion of the legal wing of the broken English language (or an outright payoff) they've "proven" to some court that the term is sufficiently ambiguous to preclude the conviction of false advertisement.