A screenshot showing them side by side would be very useful.
The most common and obvious cause of a difference between Lr and PS is a defective monitor profile, or at least one with properties that one application doesn't like.
This may show up differently between apps because, although both use the same display profile, the source profiles are very different (linear ProPhoto in Lr; 1.8 ProPhoto or something else in PS). So the actual conversion is different.
First thing to check is that your calibrator makes v2, not v4 profiles, and matrix-based, not LUT/table-based. LUT profiles can under some circumstances be problematic in Photoshop. In any case, run the calibration again.
Contrary to common belief, there is no particular reason to match Lightroom and Photoshop color settings, other than convenience. They should always display absolutely identically. The only exception to this is if you have a wide gamut monitor and one app works with sRGB and the other something bigger - then you will see gamut clipping if there is any.
A more remote possibility is a problem with Photoshop's OpenGL rendering. With the "Normal" and "Advanced" settings, Photoshop's display color management is handled in the GPU. In the "Basic" mode, or completely disabled, color management is shifted back to the CPU, which is more reliable. Lightroom doesn't use the GPU at all.