The Messenger of Allah ﷺ is the vicegerent (khalifah) of Allah ﷻ in all of the universe; in its higher realms and lower realms.
As for Prophet Adam ﷻ, he was made by Allah ﷻ as the vicegerent on the earth only. Allah ﷻ said, "Verily I am going to place a vicegerent on the earth", [Quran 2:30].
And for Prophet Dawud ﷺ. he was made as the vicegerent on the land of al-Sham: "O Dawud! verily We have appointed thee a vicegerent in the earth", [Quran 38:26]. (Here, the word (أرض) or land refers to the land of al-Sham).
Shaykh Sayyid Salah El Din Tijani R.A
اللَّهُمَّ صَل عَلَى سَيِّدِنَا مُحَمَّدٍ ۞ الفَاتِحِ لِمَا أُغْلِقَ ۞ وَالخَاتِمِ لِمَا سَبَقَ ۞ نَاصِرِ الحَقِّ بِالحَقِّ ۞ وَالهَادِي إِلَى صِرَاطِكَ المُسْتَقِيمِ ۞ وَعَلَى آلِهِ حَقَّ قَدْرِهِ وَمِقْدَارِهِ العَظِيمِ ۩
May Allah busy us and you with Allah. May Allah give us and you success in that which Allah loves and that with which He is pleased. May Allah unite our hearts and yours upon Allah. May Allah guide us and you to to straight path. May Allah cause us and you to traverse the paths to salvation. May Allah provide us and you with perfect iman, love, ma'rifah, and steadfastness upon the Sharia of Allah's Messenger Sallallahu alaihi wasallam