The "c" in 25c is millimeters. But millimeters kinda like the centimeters of an exercise ball. A "65cm" exercise ball is rarely gong to be inflated to 65cm (unless that owner is obsessive). Tires widths depend on inflation, age, rim width and manufacturer (and probably batch ).

25c is proper nomenclature but we don't say my tire is 2c bigger than yours.

And to the OP's question re: putting the 23c on in back - if it were me, I;d look first at the conditon of the 23 yo intend to put on. Is it new or in good shape? Yes? Put it in front. No? put it in back but be awre it needs significantly higher pressure because 1) it is in back, not front - I put 2-5 psi more in rear tires and 2) it is a smaller tire so has less air volume and therefore needs more pressure to ensure you do not bottom out and pinch flat or damage the rim or both. I use 5-7 pounds more in 23c tires than 25c.

Now, if you are racing, the old "rule" was that you always put your best, fastest rolling tire in back where it made a real difference. Those who wanted to win would put the 23 in back (assuming both tires were equal quality).

So like a lot of the cycling dilemmas, the answer is really simple, summed up as "It depends".

Ben