Not only do the Elohist and Priestly sources disagree on whose staff we’re talking about: Moses’ or Aaron’s (#91), but they also use different terms when it comes to describing the serpent or snake it turns into. In E (4:3) the staff becomes a snake (nahash), but in P (7:10) it becomes a serpent (tannîn). Each author chose a different term, and the Priestly writer might have even had a reason for changing nahash to tannin.
Furthermore, in E it was supposed to be Moses who was to produce this sign with his own staff (4:17), but in matter of fact, in P (7:10, 7:19, 8:1) it is rather Aaron who produces the sign, and contrary to E’s account where Aaron performs the sign in front of “the children of Israel” (4:29-31), P claims that Aaron performed the sign with his own staff and in front of the Pharaoh and his servant (7:10)! But we are getting ahead of ourselves here. More about how and why P rewrote E in the forthcoming contradictions.