Yes, Black Adam's abilities were not like Frank's and the others', drawn from Greek or Norse mythology. The magical contracts of Shazam were signed with many different kinds of gods, and what Black Adam inherited was the Power of Six Gods from Egyptian mythology.
It was precisely because Black Adam's divine power did not share the same source as Frank's and the others' that Clark had not recognized where Black Adam's divine power came from when he first saw him.
After all, although Clark had gone to Heliopolis with Robet, and Moon Knight of the Avengers was even the agent of the Egyptian Moon God Khonshu, making him something like a little Shazam who had received the power of one god, Moon Knight did not have much of a presence among the Avengers. And when Robet and Clark had gone to Heliopolis, Heliopolis had been little more than two or three strays left over. There were barely any gods remaining at all, nor any true powerhouses. It had not even compared to the fallen Asgard.
On top of that, none of the gods in Heliopolis were among those who had granted Black Adam his power, so it was perfectly normal that Clark had failed to recognize the divine power on Black Adam.
And now, the reason Black Adam had thoughts after seeing Heliopolis was because he had witnessed the power of the Avengers and wanted to see whether he could continue increasing his own strength through the gods.
In Black Adam's view, after thousands of years of development, if the Official Agencies among humanity and the Avengers could become this powerful, then the gods who had already been immensely powerful back then could not possibly have remained unchanged.
Especially after Black Adam saw that the Age of Gods had been