The same design will look different depending on whether it is on a screen or it is printed. This is because the two use different colour making models: CMYK and RGB. They work in different ways so the results will also differ based on the model you are using.
RGB stands for red, green, blue and it is a colour model where these three colours are blended in different ratios in order to get a much broader array of colours. It is referred to as the additive model because it involves combining different wavelengths in order to create new colours. It starts off with black, which is no colour at all, until it ends up at white.
This is the model that is used for screens. This means that it is the one you see whenever you watch an image on a television, computer screen, phone, tablet etc. However, this is not to say that it will be the same in all these circumstances. Each device has a different ability when it comes to rendering RGB code so it is likely that the same image will be similar, but not completely the same on two different devices. This is most obvious when you are in an electronics store and you see all the television sets lined up, showing the same footage, yet you can clearly see differences in colours and contrasts between them.
CMYK stands for cyan, magenta, yellow and key (black). Unlike RGB, this is a subtractive colour model, meaning that you start off with white and add more colours until you finally reach black. This is the model used for printing purposes. Although the image will differ less from one device to another, there will still be a difference caused by the printers and the quality of the inks. In order to get better quality, the dpi number needs to be high. This stands for dots per inch and the more dots there are, the higher the resolution is. Halftoning is also an important process here which allows for various shades and saturations to be achieved.
There will always be a difference between screen and printed designs. When you first see them, they are on a computer, meaning that they use RGB. But when they get printed, the information needs to be converted for the CMYK model. While the two will be similar, it is common for them to not match up perfectly.
Then there is also the Pantone Matching System that could prove of use. Patented in 1962, this system created a reliable set of guide from inks and pigments so that it is now able to accurately match colours regardless of the model used and the equipment used to create those colours.