Print does not emit light. A screen is actively sending out light to your eyes, a print has to do it with the level around it while viewing.
You’ll read a lot that is recommended to calibrate your monitor to around 100 nits (forget about modern HDR in this case), because that is somewhat the average level people said.
Of course, the light level is different depending on where and how you view the print. Dark attic at night or outside in bright sunny day are quite different ambient light levels.
But setting your monitor brightness to be around 100 nits helps and getting a feel for how bright something is going to look when it is not emitting light of its own (like a print).
You’ll notice a lot of pictures look too dark to your liking when you turn your monitor brightness down.
Also, even a good photo printer needs calibration. And that must include the paper you are printing on. The base color of the paper and how much ink it soaks in can have quite a different effect on white balance and color response, at different parts in your print.
Just chucking stock A4 letter paper in there, versus glossy photo paper is going to be a real difference. But unless you calibrated the printer neither of those can be ‘correct’, just different.
A printer that is meant die printing photos (even a cheaper one) can come with some kind of calibration profile, but then they are made for the branded paper that they want you to use. If you put different photo paper in to what you are ‘meant’ to do, it’s going to be different. Not worse or better, just different.
This is what the soft proofing options are for in photo tools, to emulate how something might look on another device, mostly prints.
I have a cheap Canon Selphy photo printer, nice to print quick easy 4x6 for people after a family event or party or something. But it has way less saturated reds. Something Canon does for protecting skin tones maybe, but it’s very noticeable. If I want to make a B&W print I actually have to send something with a red cast to the printer, because the printer will have less ‘red response’.
But I have a profile for it. So I don’t normally have to mess for it, I print with that printer profile so the colors get modified while printing to compensate for the color response of the printer.
Of course, you can’t compensate for everything. That’s where the soft proofing comes in. If I soft proof a picture for printing on the cheap Selphy, I know when the red saturation has reached a limit where the printer can’t do more. When I keep trying to make a photo more colorful, I’ll notice that at a certain point, the red will stop being more saturated because the printer simply can’t make it more red. So I see the saturation being skewed, while with soft proofing off you’ll not see that unless it’s ‘too late’.
Now, this is a cheap printer so I don’t really soft proof and care a lot about it, it’s just for fun quick prints. But it does highlight perfectly why a start to end calibrated workflow exists. You can then trust (for quite a bit) that what you will see on your screen is what will be on paper in the end, and you can make edits with the limitations of your final output in mind.