This make sense to you?
I’ve never actually heard that idiom, but my initial impression was of two very different things.
When I researched it, though, some sources explain it as simply two very different things, while others elaborate on that definition as two things that might possibly be confused but are in fact very different.
There seems to be agreement that it originates around 1393, according to these citations from various web pages
The earliest example — from John Gower’s Confessio Amantis of 1393 — suggests that some shopkeeper was making an illicit profit by adulterating his wares:
“And thus ful ofte chalk for cheese he changeth with ful littel cost”.
And thus ful ofte chalk for chese
He changeth with ful litel cost,
Wherof an other hath the lost
And he the profit schal receive.
The buyer was surely undiscerning; though some British cheeses are rather chalk-like in appearance, substituting more than a tiny proportion of cheese with chalk wouldn’t fool anybody for very long.
By the sixteenth century, the phrase had become a fixed expression. Hugh Latimer wrote rather sarcastically around 1555: “As though I could not discern cheese from chalk.”
Some sources cite it as British/Australian vernacular, which explains why I’m not familiar with it.