I designed a logo which has greenish colors, i printed a CMYK color proof, and the client likes the colors on the printed sample. I need to give him RGB versions of the logo for web use but here's the problem: On my hp laptop monitor the colors appear blueish, on a desktop samsung monitor the colors appear greenish (close to the printed sample). What should I do about this color difference between monitors?
I just want to add a bit of illustration to Kurt's answer, which I think is complete (+1).
When I was a kid I had a (very depressing) book about a selfish girl. She would not share her toys. In particular she cherished her crayons. One day, the boy that shared her table at art class wanted to draw a tree but had no green crayons in his pencil case. The selfish girl had plenty of green crayons but she would not share them with her unfortunate classmate. As a result, to much of the boy's distress, he had to use a blue crayon instead of a green one to draw the tree foliage (which I found quite creative but the teacher found outrageous and created quite the drama at the art class).
The CMYK vs RGB differences always remind me of this story. Take a look at this image. It depicts, in a simplified way, the RGB and CMYK colour spaces vs. the whole spectrum of colours visible to the human eye. As Kurt indicated, you will see that there are some colours that can be reproduced in CMYK but not in RGB, and viceversa.
At close inspection you will notice that there are many green colours that can be reproduced in RBG but do not exist at all on CMYK. There are some bluish greens in particular that exist in CMYK but cannot be reproduced in RBG. It seems to me you are working with one of these "CMYK only" greens.
Green and blue are the colours from hell when it comes to CMYK vs RGB consistency. There are other colours that cannot be reproduced consistently between both spaces, as you can see in the image above, but green is particularly noticeable because its is the iconic colour of vegetation. You might have noticed this problem yourself when you see pictures of beautiful meadows reproduced in your local newspaper where the grass has a cold blue hue instead of fresh green one. This is due to the Cyan ink (the C part of the CMYK) which is quite flexible but particularly weak.
Like in the crayon-hugging girl story, there is nothing you can do to fix the problem but, like the boy did, to creatively select a different colour. If you don't have the right crayon available there is nothing you can do to reproduce that colour. You have to select a different colour for RGB.
You could also, of course, restrict yourself to using only the colours that are common to both spaces, but since your client already fell in love with the CMYK only green, this does not seem like a feasible solution.
Your problem has two parts.
Part 1: CMYK colors are used for printing, RGB colors are used on screens. It is not trivial to get the same color on both mediums. And some colors are only available for RGB or only for CMYK.
So colors needed to be "translated" from one color scheme to the other. This translation is not error free (rounding errors for the calculation).
Part 2: If you want your screen to show the "right" color you have to calibrate it. There are special screens and instruments you have to use to calibrate your system. They are expensive and you have to do this several times a year.
For example, you can change the brightness of your screen, but that results in a different color shown on your screen.
Result: It is nearly impossible to show the "right" (I mean well defined) color on an uncalibrated monitor. And with an uncalibrated system the color which will be printed is not the color you saw on screen. (So the best way is to make a test print to see the resulting color, then change the color in your file to come nearer to the color you want to get on the printer. The color you then have on screen can differ much from the color on the printer ...)
I hope you can understand my poor English and I could help you better understand how colors are built on screen or printer.