No they are not. Allah was one of hundreds of pagan gods already being worshipped at the site of Mecca long before Islam came along. The murdering psychopath conquered Mecca and destroyed all gods, save one. The kaaba and the black stone were a holy site for the pagans, and it has nothing to do with the Abrahamic God.
If you go to a Christian church anywhere in the Middle East.
The services are conducted in the Arabic language and their Bibles are written in Arabic.
In their Bibles the word "Allah" is used for the word God.
An example would be:
John 3:21 "But whoever lives by the truth comes into the light, so that it may be seen plainly that what he has done has been done through
Allah."
The moon god during and before your false prophet's time was considered the chief of all the gods. Thus was given the tile of Al-ilah "the deity". This pagan god was so prominent many Arabs named their children after it. His own father had Allah in his name, named after the moon god. The moon god's idol symbol was the cresent moon. Which is why Islam is still associated with the cresent moon.
It was the only way to get the Arabs to accept his newly made up religion. "There is only ONE god worthy of worship ( as opposed to the other 360), and his name is Allah (Just like the chief of the gods you already worship, so I am not taking away your top god, how convenient!)."
Since then Muslims have just associated the title of "Allah" to the Christian God, but it is not the same that they worship.