Is Al-Aqsa Mosque different from the Dome of the Rock, and why is the Dome used as a symbol for Al-Aqsa Mosque despite this confusion among many Muslims?

The blessed Al-Aqsa Mosque is the first of the two Qiblas and one of the three mosques to which journeys are undertaken. It was built or renovated by Solomon (peace be upon him), and it existed 40 years before Solomon, after the Sacred Mosque (Al-Masjid al-Haram (definition)). The Prophet (peace and blessings of Allah be upon him) was taken on a night journey to it and led the prophets in prayer there. The Dome of the Rock was built by Abd al-Malik ibn Marwan in the year 72 AH, and it is part of the Noble Sanctuary of Jerusalem (Haram al-Qudsi al-Sharif). However, today, Al-Aqsa Mosque is the large mosque located south of the Haram courtyard. The Dome of the Rock structure is situated in the middle of the Al-Aqsa Mosque courtyard. The mosque, which is the place of prayer, is not the Dome of the Rock. In ancient times, the name 'mosque' referred to the entire courtyard. Al-Aqsa Mosque is the name for the entire mosque built by Solomon (peace be upon him), and the prayer hall (musalla) built by Umar ibn al-Khattab at its forefront is better for prayer. Neither Umar nor the Companions prayed at the Rock, and there was no dome over it during the eras of the Rightly Guided Caliphs. Jews and some Christians venerate the Rock, and it is not part of the Muslim religion. The widespread image of the Dome might lead to confusion between it and Al-Aqsa Mosque, and this could be a cunning plot by the Jews to delude Muslims into believing that Al-Aqsa is the Dome, to facilitate the demolition of the true Al-Aqsa Mosque.