Gief can SPD vs DPs because they’re not completely invulnerable. For example Ryu is completely invulnerable for the first 3 frames, but is on the ground for like 7 more after that during his Jab DP (still hits, but vulnerable low, as mentioned above), so there’s a window where he can be grabbed.
You might be able to do the same vs Strong/Fierce DP- I’m not sure if it’s because you can grab stuff that’s invulerable in A3, or because there’s a frame where they’re still on the ground. Even in OG SF, if you SPD and DP on the exact same frame, shotos will get grabbed.
Quoted for emphasis. Priority is just the simplified term most people use to explain hit boxes and their invincible properties. When a move beats another, it usually has to do with speed (one move reaches the other before it has a hit box out), or invincibility (moves that have invincibility on their hit boxes).