: Is "stock progression" the common way to write about a set chord progression? Moreover, would "stock progression" refer to a standard chord progression, say, I – VI – IV – V for a doo-wop song, or does it refer to a

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I would say there are varying levels of naming.

'Stock progression' is just generic terminology, but the meaning is perfectly clear: commonly used progressions. Lots of synonymous terms are used like harmonic formula, standard progression, etc. Sometimes a specific term is used within a particular text like schemata which is used in Music in the Galant Style. This web site calls the common patterns "money chords."

Some particular progressions are so commonly know they have their own generally universal names...

12 bar blues
Rhythm changes
La Folia
etc. etc.

...there can be variations in these progression despite them being thought of as 'standard' progressions.

In reference to I vi IV V you could call it 'stock progression' or you could be more specific and say 'doo-wop progression.' Either way you will probably end up needing to list the chords whether for performance or analysis.

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'Stock progression' is a way to talk about a standard chord progression, of which there are several - I v IV V, I vi ii V, 12 bar blues, Andalucian (Spanish) sequence, for example.

But it's pretty vague, as each needs defining. As in 'It's a standard 12 bar in A', or it's 1950s doo-wop. But even that often isn't quite enough. What's a standard 12 bar? Does the 2nd bar stay on I or go to IV? Is doo-wop I vi IV V, or maybe I vi ii V?

So, it's a generic term, but a very vague one, hardly worth the trouble!

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It means a common chord progression. Like the one you mention. (Assuming you meant I, vi, IV, V. A major VI would be rather less 'stock'.)

It's not a precise technical term, so don't over-analyse it. There isn't just one 'stock progression' for any era or any style.

The term is used and illustrated quite well here:
openmusictheory.com/popRockHarmony.html