Pharaoh or King of Egypt?

Question

In parashat shemot, how come pharoah is sometimes called the "king of Egypt" and sometimes called "Pharaoh"? The term Melech Mitzrayim appears in the Bible close to fifty times, while the word Pharaoh appears 274 times! In six cases, both names are used together: Pharaoh Melech Mitzrayim (Ex. 6:11; 6:13; 6:29; 14:8, I Kgs. 3:1, and Ezek. 29:2).

Answer 1

excerpted from here

• The Zohar (Shemot 17a; 19b) explains that in most of the opening story of the Book of Exodus, the Bible mentions Melech Mitzrayim. This refers to the angelic minister who represents the Egyptian nation in the Heavens. On the other hand, when the Torah refers to Pharaoh or Pharaoh Melech Mitzrayim, this refers to the human king of the Egyptians. Following this approach, the Zohar explains that when the Torah reports “…and Melech Mitzrayim died…” (Exodus 2:23), this does not refer to the death of the earthly King of Egypt, but to the removal of the Egyptians’ Heavenly minister from its prominence. Only once G-d demoted the Egyptians’ Heavenly representative did He begin to listen to the Jews’ prayers for redemption.
• Rav Chaim Kanievsky offers a comprehensive discussion about the three different ways in which the Bible refers to the Pharaoh. He explains that when the Pharaoh was acting on behalf of national interests, then he is referred to as Melech Mitzrayim. In contrast, when Pharaoh’s actions are motivated by his own, selfish interests (be that his self-aggrandizement or simply his pathological stubbornness), then he is called Pharaoh. When both of these factors played a role, then the king is known as Pharaoh Melech Mitzrayim.

the author does not cite the location of R' Kanievsky's comments