Step 1: Understanding the Concept.
Two different questions are hiding inside aircraft stability. First: right after a gust or control input disturbs the aircraft, does the aerodynamic moment push it back toward trim or away from it. That is static stability. Second: once that initial push happens, does the resulting motion settle down or grow over time. That is dynamic stability.
Step 2: Key Formula or Approach.
For longitudinal static stability, the condition is $\dfrac{\partial C_m}{\partial \alpha} < 0$ together with a positive $C_{m,0}$, so a positive perturbation in angle of attack produces a restoring, nose down, pitching moment. This is a single instant, single sign check. Dynamic stability instead needs the full equations of motion to be solved; a mode is dynamically stable only if its time response, something like $e^{\sigma t}\cos(\omega t + \phi)$, has $\sigma < 0$ so the envelope decays.
Step 3: Detailed Explanation.
Because the static check and the dynamic check are mathematically different conditions, one is the sign of a slope at $t=0$, the other is the sign of the real part of the eigenvalues of the linearised equations of motion, satisfying the first does not force the second. A well known case is the phugoid mode: many statically stable aircraft still have a phugoid mode with a very small or even positive $\sigma$, giving a slowly growing long period oscillation, which is dynamic instability, despite passing the static stability test. This directly makes statement (A) false and statement (C) true. Statement (B) is simply the correct definition of static stability restated, and statement (D) is simply the correct definition of dynamic stability restated, so both are true.
Step 4: Final Answer.
Statements (B), (C) and (D) are true; only (A) is false, since static stability alone cannot guarantee dynamic stability.