**Core Concept**
Skeletal and cardiac muscles are two types of striated muscles with distinct physiological properties. Excitation-contraction coupling refers to the process by which muscle contraction is initiated and regulated. Calcium ions play a crucial role in this process, acting as a second messenger to trigger muscle contraction.

**Why the Correct Answer is Right**
Graded contraction is a characteristic of smooth muscle, not skeletal or cardiac muscle. Skeletal muscle contraction is an all-or-nothing phenomenon, where each muscle fiber contracts maximally or not at all. Cardiac muscle contraction is also all-or-nothing, but with a slight variation in force depending on the frequency of stimulation. In contrast, smooth muscle can contract to varying degrees depending on the strength of the stimulus. Therefore, option C is false because both skeletal and cardiac muscles do not have graded contraction.

**Why Each Wrong Option is Incorrect**
**Option A:** Both skeletal and cardiac muscles require calcium for excitation-contraction coupling, making this statement true. Calcium ions bind to troponin and tropomyosin, causing a conformational change that exposes the myosin binding site, leading to muscle contraction.
**Option B:** Skeletal muscle excitation-contraction coupling is actually dependent on extracellular calcium, which enters the muscle cell through voltage-gated calcium channels. This statement is false, making option C the correct answer.
**Option D:** The plateau phase is indeed seen in the action potential of cardiac muscle, which is unique among muscle types. This phase is caused by the opening of the slow inward calcium channels, allowing a sustained influx of calcium ions and maintaining the muscle contraction.

**Clinical Pearl / High-Yield Fact**
It's essential to remember that skeletal and cardiac muscles exhibit all-or-nothing contraction, whereas smooth muscle exhibits graded contraction. This distinction is crucial in understanding various physiological and pathological processes.

**Correct Answer:**
✓ Correct Answer: C. Both have graded contraction