1)G'virah גְּבִירָה used 6 times: 1 Kings 11:19, 15:13, 2Kings 10:13, 2 Chronicles 15:16, Jeremiah 13:18, 29:2. These are in reference to Jewish women.
2)Malkah מַּלְכָּה used around 40 times. 4 times in 1 Kings 10, 4 in 2 Chronicles 9 (all 8 concerning the Queen of Sheba). 25 times in the book of Esther (initially for Queen Vashti, then mostly for Esther). Jeremiah uses it 5 times for the pagan goddess Asherah, in verses 7:18, 44:17-19, 25. Then two times in Songs of Solomon--6:8-9. Then another 2 times at least in the Aramaic text of Daniel 5:10.
3)Shegal שֵׁגַל is used twice in the Hebrew text. Psalm 45:9(10)[called 44:10 in the LXX/Vulgate]. And once in Nehemiah 2:6. In addition it is used in the Aramaic text of Daniel 3 times, in verses 5:2-3,25.1) The term g'virah "queen-mother" typically denotes the mother of the King as with Solomon and his mother the g'virah Bathsheba, or in the case of Asa--his grandmother (2 Chronicles 15:16). According to 1 Kings 2:19, a throne was provided at the right hand of the King for his mother (who would be the g'virah). The position seems honorary, but extremely influential, since generally a man is most loyal to his mother. She does not seem to have any authority in of herself, but any she had was dependent on her relationship with her son (or grandson) the king. A type of Mary and Jesus. The term G'virah seems to be exclusively for the Jewish King's mother/grandmother.
2)Malkah מַּלְכָּה is the feminine form of the word מֶּלֶךְ melek king. In the Hebrew bible there was never a Jewish malkah over Israel/Judah, not even when you might expect it in regards to the usurping woman Athaliah in 2 Kings 11. Esther (a Benjamite like King Saul, Israel's first king), however, in her book is referred to as a malkah in the Persian empire in her time, after the king removes the original queen Vashti (Esther 1-2). A malkah seems to be a female sovereign in the Hebrew bible, just like a king, as seen by the Queen of Sheba (1 Kings 10, 2 Chronicles 9), theoretically it could just be a title alone of the King's wife, in the sense a woman in the early church was called an episcopess/bishopess, not because she was a bishop, but because her husband was one, this may also be true with the 'prophetess' in Isaiah 8:3. This may be the case with Queen Vashti in Esther 1, since she seems to be taking orders from the king, and is easily replaced with Esther by the king.
3) A shegal שֵׁגַל seems to be the more explicit term for the wife of the king. The term as a noun is only used twice in the Hebrew bible, and a few in Daniel 5. The meaning of the word has been debated for thousands of years by both Jews and Christians. Some believed it to be a crude way of referring to sex/a female dog. Others suggest its an Akkadian loan word meaning the main wife of a king, which makes a little more sense. A shegal as a noun in the Hebrew text of the bible is only used in the singular, in Daniel's Aramaic its sometimes translated in the plural as "his wives" or "his queens" other translations have "his wife" or "his queen." The term shegal does not even seem to refer to an Israelite woman, though perhaps one, if not a convert in Psalm 45, otherwise, it refers to Persian royalty. The Persian shegal in Nehemiah 2 seems to sit next to the king (on a throne?).
The terms do not seem synonymous. At times Shegal and Malkah seem synonymous as they may refer to the king's wife, but neither seems to be really a position for a woman in the Davidic kingdom. To complicate things more, both shegal and malkah in their Aramaic forms are both used in Daniel 5. The most for certain closed equivalent to a proper Jewish queen was the G'virah--the "queen mother," who would be the recently depart king's wife, and the current king's mother. If there was a Jewish shegal, she would have became the g'virah when her son became king. But certainly there never was a true Jewish malkah in the Davidic Kingdom.
**Note: There could be other words for "queen," for example the Vulgate calls the countless wives of King Solomon "regina"--"queens," perhaps not to call them queens, but wives of the King, the Hebrew word used there is sarot, which is the feminine plural of the sar, which means "prince" or "captain"