Hi! I always edit my photos in Lightroom Classic and some of them also in Photoshop 2022 (from Lightroom to Photoshop and back). Back in Lightroom, I edit them also in black and white. I notice a big difference between the black and white tones of photos that I edited in Photoshop and the ones I did not. The color photos have the same color, it's just the black and white editing. I like the ones that come from Photoshop better, but I don't know how to get the same result of the other photos that don't need to be edited in Photoshop. Does someone know what causes this change? Thank you!
Never noticed this but you are absolutely right. The difference appears to be caused by the different profile that is applied to raw files vs that that is applied to rendered images (tiff/psd/etc/) when you click on monochrome. I don't think you can fix this as it appears to be caused by how the profiles are implemented. You can try some of the creative black and white profiles to get more pleasing results but I don't think you can trivially easily reproduce the effect of black and whiting a rendered file for a raw file because of this.
If the goal is to match the results with one profile, when using another, then I agree this will be challenging or even unfeasible. The profiles will have likely been tuned to deliver independent ideas of what is pleasing, given there is no "accuracy" per se when it comes to B&W conversion. There are only a) is it consistent, and b) do I like this or not!
If however the goal is to apply consistent B&W conversions for Raw / non Raw, assuming their colour renditions look the same otherwise - that is I think much more possible. I like to leave images in full colour mode so far as LrC considers them. My preferred approach from there is the HSL panel. I begin with a preset which sets all of the Saturation sliders to 0. Then the Luminance sliders act to the same effect, as the Color Mixer sliders otherwise would have done in B&W mode. Hue sliders of the HSL panel and the colour specific Basic adjustments such as WB, Vibrance and Saturation remain usable too, varying what the B&W conversion's own response, "sees" as the hue information of the image. That's a bit more hard to visualise, but the main HSL panel Luminance sliders are intuitive IMO, plus you can use the targeted adjustment tool to good purpose there.
The settings of HSL are file type independent, hence can be synced between Raw and non Raw images / applied via a preset (Color Adjustments checkbox) indiscriminately.