If you mean the homing attack, spindashes, possibly the spring, yeah. They are.
That said, Sonic was expanded upon quite a bit to fill out his input slots as a Smash fighter. Where Sonic kicks, Shadow has jets. Where Sonic punches, Shadow could condense energy(like in Sonic Fighters). Shadow’s first appearance in the villain playthrough of Sonic Adventure 2 shows him hovering in midair. Shadow can also use singular Chaos Emeralds to manipulate time and space.
They do play exactly the same(although run animations were slightly differed mechanically) in most iterations, but he could easily be expanded upon creatively.
I’m guessing no, because of the reasons you list above. But it is something to consider that in other titles, Sonic and Shadow have had major gameplay differences, especially in Sonic fighters and Shadow’s own game.