Rare vs uncommon

What criteria does one use to ascribe a rarity status to a stamp?

There is no consensus.

Is it the very scarce number of the particular stamp or postmark in existence?

Or does it pertained to a much desired item, tightly held, such that it is not easily acquired?

However, the rarity of an item does not equate to value.

It all depends on the desirability, the difficult in acquiring and the so called market forces.

For some popular countries like GB and USA, their stamps are always going to be more desirable and more valuable in general regardless of scarcity.

Where an individual stamp is concerned, condition, condition and condition dictates value unless it is unique.

I would personally consider a stamp or postmark to be rare if only a score or so copies are in existence and very rare as less than ten.

Otherwise, it is generally safer to describe such items as uncommon or very uncommon.

And some rare examples in our territories would include:  

North Borneo, SG1a imperf between horizontal pair-2 copies

North Borneo, SG54a large "s" in "cents" overprint-1 copy etc

North Borneo postmarks, Sipitang,  Jesselton BNBC, Gantian, Kudat P and cancelled at Brooketon etc

Labuan SG 22 "One Dollar A.S.H.", SG142 $10 Labuan overprint etc

The famous Labuan 8c postage due frame inverted, using the criteria, can only be described as very uncommon. It maintains its value very well because it is probably the most popular stamp of Labuan.

Straits Settlements, Hong Kong and Indian stamps used at Labuan, Labuan D1 and D2 etc

Brunei prewar Seria and curved year Belait and Tutong cancellations etc

Sarawak 1876 "TWO CENTS" surcharge on SG2 etc

Sarawak early manuscript town cancellations, Betong type 1, Paku, Pusa type 1

etc

These are some obvious candidates and is definitely not a comprehensive list.

What is rare today may not be so in the future due to continuing new discoveries.
On a similar vein, readers may like to read a posting from a few years ago discussing "What is a postmark?" by clicking on the link here.