This is a very complicated question because of the technicalities involved. I’ll try to simplify it greatly. Basically? It’s not what you look at that matters it’s what you see, and every computer displays your image differently.
So somehow we need a standardization. Enter Adobe sRGB 1996 which is a colorspace developed for all computers and televisions, in you guessed it, 1996. The sRGB color space is MUCH smaller than we can both see and print. Even still different monitors will display these colors differently, that’s why you see so many differences at the TV store.(and another reason why they show the same image on all screens now)
The image above shows ALL of the colors, then the red triangle shows you the sRGB colorspace and the yellow Triangle shows the Adobe RGB 1998 color space which is MUCH larger. Even larger than that is the whole color space or ProPhoto, BUT there is currently no monitor, or printer, or paper that can show you all of the colors in ProPhoto!
My position? If you can’t see it or print it? Why worry about it? There are shit tons of arguments about this subject all over the internet…. but remember my position! If nobody can see it on their monitor or print it? Why do we need to worry about it? Also? There are currently zero attempts being made to give us the capability to view ProPhoto on a monitor, or allow a paper to absorb all of those colors.
Enter Apple Display P 3
In 2015 Apple introduced their consumer 27″ iMac with a monitor that reproduces 100% of the colorspace DCI-P3 defined in 2005. Apple calls theirs DisplayP3.
As you can see in the image above Apple P3 is very close to Adobe RGB 1998, BUT! It’s actually developed more for video. This colorspace shows different greens, yellows, and reds. Their monitors are also VERY bright. If you turn down the brightness of an Apple monitor to 40% you will get real close to Adobe RGB 1998. But still not be exact. This is one reason why if you show the printer the image on your iPhone or iPad, it will not look the same. Especially if the brightness is turned all the way up.
The Very Best Way To Print What You See Is An RGB Monitor!
If you use a RGB monitor and calibrate that correctly you will get a print of exactly what you see. From here your lighting in your office matters as well, along with some other factors. Such as editing your images as a 16 bit tiff file with your editing program set to Adobe RGB 1998. If you edit your images as an 8 bit jpeg? You will be editing that image with only 20% of the information possible… so WAY less quality and color.