According to the following link https://en.wikipedia.org/wiki/Royal_family_of_Emesa
Emesa was famous for the worship of the strong ancient pagan cult El-Gebal, also known as Elagabal.[1] The city was renowned for El-Gebal’s place of worship the Temple of the Sun. El-Gebal was worshipped in the form of a conical black stone.[1] El-Gebal was the Aramaic name for the Syrian Sun God and means God of the Mountain.
Is there any relation between these two black stones ?
No, the similarities are only superficial.
The black stone in the Ka’aba is far older and has a different origin. Also the form of worship and beliefs is quite different between Muslims and the Elgabal.