Devata Artifacts had souls. The souls were called artifact souls. Since they were born from Devata Artifacts, they were called natural souls as well.
As for Celestial Weapons and Celestial Supreme Treasures, they did not possess souls. It could only seal living beings who would then become 'souls' of the weapons or treasures.
For example, Elder Huo was sealed in the Seven Treasures Exquisite Pagoda. That was how he became the pagoda soul of the Seven Treasures Exquisite Pagoda. He was known as what was called an extraneous artifact soul.
Although an extraneous artifact soul was not born naturally from a Celestial Weapon or Treasure, it would not be able to leave until the owner of the weapon or treasure removed the connection between the soul and the weapon or treasure it was bound to.
On the other hand, natural souls were able to come and go freely. They could leave the artifact they were born from and roam around the world unfettered.