Shiva and Shankar (Śaṅkara) are commonly used as names of the same revered deity, and Sanskrit dictionaries explicitly record Śaṅkara as an epithet of Shiva. Yet some theological or teaching traditions distinguish the terms. For example, a teacher may use ‘Shiva’ for the unmanifest supreme principle and ‘Shankar’ for a personally accessible, manifested form.
That distinction is meaningful within the tradition making it, but should not be projected onto all Hindu or Shaiva thought. Other devotees and texts freely use both names for the same divine being without marking two separate ontological entities. ShivGoraksh should therefore maintain separate learnable terms and tradition-qualified claims where useful, while avoiding an unsupported universal verdict that Shiva and Shankar must either always be identical in every sense or always be two distinct gods.