The first place I would check would be whether the two areas are indeed the same. Black should be 000000 on the color code. On the monitor, you could have 010101 and it would still appear black but the printer might see it differently. This was an old trick on a lot of games where a color such as blue minus 1 is defined as being transparent. You can't tell the difference but the computer sure as hell can.
The other is whether the printer is properly calibrated(?). This is something I don't really know how to fix. There is a printer at work that I use, sometimes, for printing out true black images but for some damn reason if I don't have the mean(?) average the same across the sheet, then the printer doesn't keep the whites truly white but grays them out a bit. I'm not entirely sure what happens there.
I've seen similar effects on ink based printers but the effect is inverted. It's the color that's getting lost. I'm not entirely sure what causes that either. Replacing the ink heads sometimes helps, sometimes not. Some printers do have a setting that forces the printer to pause between each "line" to allow the ink to settle/dry/whatever that seems to help on intense colors. I've only seen a few printers come with that option though. I think photo is supposed to have that option built in but.... well

TBH, I don't do a lot of printing outside of tests or documents.