How could these 2 screens have the settings and are the same model, yet the colors are extremely different and the difference between blue links and purple links is not clear in the one in the right?
This is entirely normal. Uncalibrated monitors really work like this, no two monitor being alike. In fact even if you calibrate them they will slowly drift appart over time. So calibration is something you need to do periodically, with a hardware calibrator (no software will not do).
RGB color values are devoid of meaning without the knowledge of that their profiles are (measurement of what the device shows). Preferably multi monitors should be calibrated to the same profile. Best would be to chose a standard that your monitor can safely attain.
Welcome to the wonderful world of accurate color. Where even the room wall color affects how you understand the color on your screen.
PS: The lesson to learn here is that if you choose colors for web, dont waste too much time on the exact hue, as most monitors are sub par, and not calibrated. So one can not expect others to see the exact same color.
We've come across this problem a lot because everyone in the office has at least two monitors.
There can be a number of causes we've found:
The monitors have different colour settings.
On the monitor itself, there are usually multiple options that adjust the monitor display settings - there can be colour profiles, custom profiles for RGB channels, settings for luminance, brightness, contrast etc - these all need to be exactly the same. One quick way of doing this is to reset the monitors to factory settings, providing they have the same firmware (very very likely) this should reset all settings on both screens to the same settings.
The monitors are running off different graphics outputs
We've had this a lot where one monitor will be running off VGA and the other off HDMI. Now by default a lot of PC's (can't speak for Mac) will run the VGA port off the built-in Intel graphics, and other ports such as HDMI, DVI etc will run off the graphics card. This can get intricate, but to start with, try swapping the monitors over to different ports and seeing if the colour changes. The best thing is to use two of the same type of ports to power both monitors, this will almost certainly mean that the outputs from the ports will be identical in colour and quality. If the computer doesn't have these, using a docking station can enable you to get extra ports as required.
The colour settings are set differently within the PC software
Most graphics software will have the option to set different displays to different settings - you can individually tweak the colour, resolution, refresh rate, brightness etc of each monitor. It's unlikely they are different unless someone has customised them specially, but it's worth double checking to make sure.
The monitors are running off different display formats
Similar to the one above, but even if VGA and DisplayPort are being output from the same graphics card, because the signal type is a different format, this can result in some discrepancies, although "theoretically" it shouldn't make a difference (one or two cases it certainly has though). Again, it's best to match the monitors to the same type of port.
Different quality monitor cables
HDMI alone has many variations - HDMI, HDMI with ethernet, High Speed, and High Speed with ethernet, to name a few. And then you have variations with DisplayPort, DVI, and Thunderbolt connections are starting to come in... Differences in cable type, variation and quality can result in differences in the quality of what you see on your screen. Ensure the cables are identical, and undamaged.
The monitors age or use could have changed the way it looks
If the monitors are a different age, ie, one bought months before the other, or one has had some rough handling, this could affect them.
Let us know how you get on, I've listed all the problems we've come across!