the two targets will lay on the same plane during runtime (when they are recognized and detected by the AR engine) if the AR engine considers them on the same plane;
i.e. it is the Vuforia engine which determines the actual position (and orientation) of the targets, once it has detected them;
one thing that may affect the fact that you don't see them exactly on the same plane could be if the two targets have different Size parameters, or maybe if they have the same Size but you print them on paper with slightly different size (e.g. are they both printed with the same scale, for example both on an A4 paper ?)
For example, if your targets both have the same size (in Unity), but you print one of them with a slightly larger/smaller size, then Vuforia will estimate the pose of the printed target as a bit closer or farther away from the camera (with the resulting misalignment that you observe).
Or, if the two targets have different Size in unity, this can also lead to different pose estimation if such size difference is not accurately refelected in the real (printed) targets.
I hope this makes sense to you.