Physical Clocks: Correctness vs. Accuracy

In the context of studying for a class on distributed systems I stumbled upon the following definitions that I do not understand:

• Let C(t) be a perfect clock.
• A clock Ci(t) is called correct at time t if Ci(t) = C(t).
• A clock Ci(t) is called accurate at time t if dCi(t)/dt = dC(t)/dt ≡ 1.

Question 1: I do get what the definition of correctness means, but how is accuracy different from it?

Question 2: What's the d all about? A not so mathematical explaination would be much appreciated.

Thank you very much in advance!

Without more symbols, but mathematical conceptually: Accuracy means your clock is changing at the same rate as the perfect clock. Correctness means the clocks register the same time. d is derivative - you can check a calculus book, or wikipedia. t means time, so change of the imperfect/perfect clock with respect to time.