How a pendulum accelerates? I have learned that $-g\sin\theta$ describes the acceleration of a pendulum. But surely if a pendulum is held from a point, say this point is $a$ and another point $b$ and say suppose that point $a$ is higher than point $b$, upon dropping the whatever object is attached to the pendulum, and within both scenarios, each ball must stop at a given point, and this point is the same for whatever point they are dropped from, say, point $c$, therefore dropping the ball from point A must ultimately accelerate more than point B since it is under influence longer from gravity.
So I figured, $-g\sin\theta = a$ ( sorry for the ambiguity, here $a$ is acceleration of course ), doesn't necessarily work in this case. Could we view the pendulum motion as individual discrete gains in energy due to gravity and then integrate it to achieve the accumulated energy at point b?
So perhaps something like,
$$\int_a^c -mg\sin\theta d\theta$$
 A: The tangential acceleration of the mass is solely determined by it's angular position $\theta$ by what you say: $a_\bot=-g\sin\theta$. There is no velocity dependent forces in the scenario you describe, so the acceleration will not depend on the velocity as well.
If an object is released from rest at $\theta_A$ and another object is released from rest at $\theta_B<\theta_A$, then when mass $A$ reaches $\theta_B$ it will indeed have a larger velocity than mass $B$ at $\theta_B$, but they both will have the same tangential acceleration at $\theta_B$ because the tangential acceleration is a function only of $\theta$.
A simpler example of this is a ball that is dropped from your hand versus one that is thrown from your other hand. Once both balls are released they will have the same acceleration ($g$ downwards) even though their velocities are different.
The more general misunderstanding here is that a larger velocity means a larger acceleration must have caused that larger velocity. But this is not the case. Velocity changes over time due to acceleration, so "small" accelerations can cause "large" velocities and vice versa, but it is incorrect to assume that at some instant a large velocity means a large acceleration, or that the acceleration is solely, if at all, determined by the velocity.
