The constant in the merge sort recurrence
Nitpick: Are they really talking about time? If they are actually counting some operation, it's well possible (if unlikely) for the same constant to show up in both places.


  How is there a constant  c that can represent both times?


It (probably) can not. This is a simplification done with the goal in mind: derive a $\Theta$-bound.

Apply the Master theorem to both candidate recurrences; you'll note that the result stays the same. CLRS know this from experience, so they simplify the recurrence a-priori.