"discerning the difference" is a grammatically correct and commonly used phrase in written English.
You can use it when you want to describe the act of understanding or perceiving a distinction or variation between two or more things. Example: The detective's sharp eye and discerning mind helped him in discerning the difference between the two suspects' alibis, solving the case.
Discerning the difference between the 'reason of being' and the 'reason of becoming' is important for understanding the different ways Wolff employs PSR in his exposition of metaphysics.
Inside, outside, I was having trouble discerning the difference.
Discerning the difference between "posh" and "body hugger" denims was like trying to tell the Olsen twins apart.
He has been taking lessons from Mr. Kuhlman for three months now, discerning the difference between "birth" and "bird," reading little stories with titles like "Eddy's Night Out".
But Benedict's proposal for discerning the difference between healthy markets and pathological ones is uncompromising and offers no sops to the secular.
Discerning the difference between some benign lesions and early stage breast cancer is a particularly challenging area of pathology, according to medical records and interviews with doctors and patients.
On the other hand, a tracer with a small partitioning coefficient makes discerning the differences in mean residence times difficult.
Even if you don't personally own any of these devices, this geeky approach to discerning the differences between Apple's tablet displays at Repair Labs is worth a look.
I observed how my mind was made up of all this information, of the countless hours I'd spent studying notecards, discerning the differences between types of schizophrenia and personality disorders, between major depression and dysthymia, and on and on.
By the way, any reader capable of discerning the differences between the multiple strains of Islamic fundamentalist sentiments and explaining why how these differences warrant turning the entire Middle east into a cauldron of violence would be supplying all of us with a knowledge that has yet to be made manifest if it ever will - at least before final judgment.
