Also note that in the later portions of Super, Goku and Vegeta are specifically refered to as mortals by the likes of Goku Black, Zamasu, Shin, Elder Kaioshin, Beerus, Whis, and all the other gods.Context: After Goku has become Super Saiyan God
Gohan: "I can't sense dad's ki at all."
Whis: "That's fine. After all, the ki a god emits cannot be sensed by ordinary humans."
Gohan: "Then dad really is a..."
Whis: "Yes, Super Saiyan God. I don't know whether he's the same as Beerus-sama or the Kaioshins, but at the very least he's become as much of a god as they are."
Significance: Re-re-reinforcing the idea that non-gods can’t sense a god’s ki. Whis’ final statement is also open to interpretation. He doesn’t know if SSG Goku is “the same” (同じ) as Beerus or the Kaioshins, but seems sure that Goku has at least become 同等の神/doutou no kami, literally the “same level” of god, less literally an equivalent god, equivalently a god, the same caliber of god, etc. Whether or not this means Goku actually ranks as high as Kaioshin or Beerus in DB’s somewhat complex god hierarchy, I don’t know. Overall I think it probably just means Goku is definitely a god, as much as Beerus and the Kaioshins, but that he’s not necessarily the same type of god. If nothing else, SSG Goku doesn’t seem to have a job or position maintaining the balance of the universe and all that jazz, the way the Kaioshins/Beerus do, so the idea that he has an official rank in that hierarchy seems odd, until/unless we get further.
SSJ God does something more unique to the user than just giving him Godly Ki. It requiers a ritual to achieve it. It gives the user a slimmer body tone, darker skin color, taller height, fully formed eyes, it makes the user even more youtful and younger looking. Plus it gives them the ability to heal themselves. Aswell as several other techniques as seen in the Broly movie.
Point is, SSJ God really IS a God Form. As opposed to SSJ Blue, which does none of these things to Goku, other than giving him God ki and powering up his ki strength. It’s just Super Saiyan 1 with God ki, and nothing more.