Different calibration programs can produce different results even with the same sensor, because they use different processing and profiling algorithms. So yes, two displays calibrated by different software may not match closely.

Your camera test is not a reliable way to judge monitor calibration. A RAW file still has to be demosaiced and color-rendered before you see RGB histograms, and the camera sensor, white balance multipliers, and conversion pipeline can all shift those channel values. That means the mismatch you see in the histogram may come from the camera workflow, not the monitor.

Practical takeaways:

• Use the same calibrator software for all displays if you want the closest match.
• Control the environment: calibrate with no room light or very stable dim light, and avoid influence from other active displays.
• Don’t expect a MacBook panel and an external monitor to look identical.
• If results still seem poor, the answers suggest trying a different calibrator/software combination; Spyder was specifically criticized, while X-Rite/i1 solutions were recommended.

So the factory preset looking better in a photo does not prove it is more accurate.