No, it is different. Photon drives are like a reactionless drive in that you are not expelling matter, but photon drives are emitting mass/energy in one direction and moving in the other and conserve momentum.
Reactionless drives just produce force, pushing off "nothing." They violate conservation of momentum and break physics as we know it pretty conclusively.
I am not sure if you are joking...but one should not imagine the situation like a tiny space ship inside an egg pushing against the egg shell from within.
I think you do have a good point. Of course it's not reactionless like the EM drive, but in practice, what's the difference? Both require a power source and both can continue providing thrust forever without running out of reaction mass as long as they have that power source. Even the EM drive, if it works, would still need an RTG or solar panels or something to power it, and that would still limit its use for interstellar travel.