This is a great example. Plenty of patients can come in talking and coherent with a serum sodium of 115 while someone else can be confused and lethargic at a sodium of 125; the difference is how quickly they got there (and then, the speed of correction also matters).
Another example is systolic hypertension. Some elderly patients can live well with a systolic in the 170-190 mm Hg due to slowly increasing arterial stiffness. Take a 30 year old woman who’s pregnant (and with pre-eclampsia, for our example) and give her a systolic of 180 and her ears are ringing, she’s got blurry vision, and she has a headache.
Rate of change can be clinically meaningful.