The confusion is understandable because a lot of things seem to use phase and they all relate to P-space. The phase lance goes into P-space (but interesting its lasers can flicker as if being blocked when given a lot of power). Phase anchor will cause "immense distortion in P-space" (whatever that means, probably just something they threw in for balance?) Adaptive phase coils mention thats the reason you slow down is because you can't maintain a connection with normal space making it so the coils struggle to "gain traction." And of course we know that you have to tune or calibrate sensors and coils to make them more or less effective. The Doom codex entry mentions sensitive crew having "unnerving physiological phenomenon" during rapid phase shifts. So its possible humans and AIs are both effected by p-space (or going through p-space) in similar ways.
Phase Skimmer and Phase Teleporter have very little lore about them. With their codex entry having no flavor text and being purely explanations for the mechanic. This makes me think that the devs didn't have much lore attached to phase skimmers/teleporters meaning they may not have thought about how using the word "phase" for skimmer/teleporter would connect them to p-space phase stuff or just assumed phase skimmer/teleporter use p-space in a different less demanding way. It seems like phase skimming is much less demanding and the challenge is moving large amounts of mass than anything else hence the radiant codex entry. They could be the same technology or physics but because its less demanding humans/AIs don't get the same side effects as p-space jumping.
I suppose the moral of my write up is that it is odd they both use the word "phase". But there doesn't seem to be an explanation for if they are related or not. My (uninformed) theory is that phase skimmer/teleporter is something generic they threw together and then later they added phase ships and p-space which coincidently use the same wording but have no connection. Or they just haven't had the time/care to explain how they are similar and are too busy adding The Horrors. The one snag is Ziggy which does (?) have an AI but also seems to hate AI with you getting an event learning that after defeating ziggy is tried to kill an alpha core in your inventory. If Ziggy was using AI it seemed much better at handling p-space which could be explained by it using dorito technology.