Answer
No, Lord Shiva is not a jiva.
At the same time, he is also not identical to the Supreme Personality of Godhead, Lord Krishna.
Lord Shiva is a unique expansion of Krishna, specifically known as a guna-avatara, the presiding deity of the mode of ignorance (tamo-guna). He appears in this form to perform a particular function within the material creation.
His principal responsibility is the destruction of the material universe at the appropriate time. Although this function is associated with the mode of ignorance, Lord Shiva himself is never influenced by that mode. Rather, he presides over it by the empowerment of the Supreme Lord.
Lord Shiva performs the work of destruction under the direction of Krishna. More specifically, he is a great devotee of Lord Sankarshana, an expansion of the Supreme Lord.
When Lord Sankarshana wills the destruction of the universe, that divine will is manifested through Lord Shiva. It is then that Lord Shiva performs his cosmic Tandava dance, bringing about the destruction of the material creation according to the Lord's plan.
Thus, Lord Shiva acts entirely under the direction and empowerment of the Supreme Lord.
From the philosophical point of view, Lord Shiva occupies a unique position. He is neither an ordinary jiva nor the Supreme Lord Vishnu. His position is distinct and incomparable, lying between the category of the individual living beings and the category of the Supreme Personality of Godhead.
Although this is the technical understanding of his ontological position, Lord Shiva is fully transcendental. He is never subject to the laws of material nature, nor is he affected by the reactions of material activities.
Even though he is connected with the mode of ignorance as its presiding deity, he always remains beyond the influence of the three modes of material nature.
Therefore, Lord Shiva should never be regarded as an ordinary living entity. He is an eternally liberated, transcendental personality, a unique expansion of the Supreme Lord, and one of His greatest devotees.
