It's not the screenshot that's different - the underlying rgb values are device-independent – but rather, it looks different on every display.
Calibration is the only answer, but really, other than color critical applications, such as press matching, color matching is not as important as it may seem. Every device will display colors a bit differently. This isn't really a problem, since our eyes naturally correct for small differences, ie. you won't see the difference unless you see them side by side.
The color gamut for all monitors is a function of their luminance (ie. how bright they are), plus edge enhancements that push some chroma values further. These devices will actually suffer from color management, since trying to maintain device independent color will actually inhibit edge colors.