This is a calibration problem. Your screen displays colours not only in an other system (RGB) as your printer (CMYK+other colours if it is a photo printer), but even if you work in the same system, like having 2 screens of the same make and model, you may have differences in colour and lightness. The solution to this is calibration. You (using a a calibration program and some special hardware) measure the colours reproduced and adapt some tables, that are used to translate the colours from one media to an other. This is complex and even pros are not always doing a good job here. To complicate the situation for prints, calibration is paper and ink dependant. If you are in a controlled environment, ie it's your screen and printer, then you can try to adapt the pictures in a way, that the print is looking correct. To be clear: this is absolutely an amateurish behaviour and should be replaced as soon as possible with a calibrated workflow. Anyhow, consumer printers are optimized for sRGB colour space and RGB printing. The printer and driver are using all the necessary measures to convert such an image to a correct paper image. You still need to select the correct paper and type for the print job! And if you are using a paper that is not listed by the printer driver, you need to load the correct colour tables for that paper, when they exist. In this case you only need to provide a good RGB image. If you are taking your design to an outside printer service, you absolutely need to make sure that you meet the correct and required parameters. Probably, by adapting your image to your printer using the correct paper parameters and the sRGB colour space, an outside print will not differ much. I still recommend doing a test print. At the end, it will be cheaper then to shredder all the prints. A test print may be a picture with stripes of different brightnesses. In the good old times a similar system was used to find out the correct parameters for classic photo developing. Also, a serious service provider will give some guidance on how to prepare the picture and will check if it is correct.
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