It sounds as if your document is in CMYK Color Mode.
If you want (consistent) RGB values, you should work in RGB Color Mode.
Yes, it's in CMYK Color Mode but those values don't match either. In Illustrator it's C 88 M 78 Y 0 K 0 and Photoshop C 84 M 69 Y 0 K 0.
Verify that the Color Settings for Illustrator Program and Photoshop Program are set the same. You can unify these settings across Adobe products with Bridge.
You shouldn't expect the color values from RGB to match in a CMYK world. Understanding Gamut and Color Spaces for each color model is important if you want consistant color. If not perhaps take Jacob's advice and work in RGB mode.
edit: in addition to colors not being CMYK
The new color swatch in the Color Picker in Illustrator is not reliable for evaluating colors because it is not color managed. It is a poorly implemented feature. It works properly in Photoshop.
This is a screen shot from illustrator CS5. On the right side of the image is the color displayed in the document. The color space of the document is sRGB, the values of red color are R=255 G=0 B=0, and it appears correctly on my monitor represented with different values sent to the video card by the color management but in the new color swatch in the Color picker the values are not color corrected but sent the same to the video card or in other words using my monitor color space and not the sRGB color space.
If you turn off the color management by choosing Emulate Adobe Illustrator 6.0 from the Settings menu in the Color settings, all colors will be displayed in your monitor color space without any color management simulations and thus they will always match but not simulating anything like a printer result or a standard color space that other devices can be set to reproduce.
Okay, I realize that using the RGB values while it's in CMYK was a mistake on my point. I only did so to prove a point. Regardless of what color mode it's in (and I want it in CMYK because the image will be printed), the colors are NOT the ones selected.
For a better example- when I select a hot pink, it comes up as gray. I don't feel like any of the answers here are addressing the actual problem which is that my color picker is not responding to the chosen colors.
I've attached the screen shot with the blue issue I was having so that you can see that it's not the color selected.
Both Illustrator and Photoshop have synced color settings through Bridge.
I don't know if I'm efficiently explaining the problem here. I do not expect RGB and CMYK to be the same and that was never implied. I gave you some of the values in the color picker in Illustrator and then in Paint & Photoshop. None of the values matched because it was choosing a completely different color. I have been using this program for years now and have absolutely never encountered this problem before which is why I'm so frustrated.
I don't know if I'm efficiently explaining the problem here.
I think you can try explaining it better by giving some additional information.
What is the name of the color space (profile) listed after Monitor RGB on the RGB menu in the Working Spaces section of the Color Settings?
What are the color values of the color you have trouble with? Please provide the CMYK or RGB values depending on the color mode of the document.
Please, provide a screen shot in png file format so the colors can be measured accurately without being altered by the jpg compression.
Also please include in the screen shot the Color panel with a slider set to the color model of the document.
Also to make sure that the color in the document is not altered by any other means, like blending modes, multiple fills appearance, masks, etc. create a new document with a simple box with the same color values and check if the colors match.
If you're working in CMYK mode and you apply an RGB colour that is outside the range of your assigned CMYK space (as the vivid blue you're trying to use most likely is), then it will be converted to the nearest colour possible in your chosen CMYK working space. That's what's happening.
If you want to use colours that aren't printable in CMYK, then set your document's colour mode to RGB, but don't expect to get the same blue in print. Your printer is unlikely to be capable of it. If you want to keep within a printable range of colours, specify them using CMYK values, not RGB.