Your two screenshots are both from Develop, and are identical. However, there's a difference in the Navigator, and I don't know what you did inbetween to cause that.
But you may have a defective monitor profile, try setting it to sRGB. If that fixes the issue, you should ideally calibrate the monitor with a hardware calibrator. (for instance Spyder or ColorMunki) This will create a new monitor profile that accurately describes your monitor.
Go to Control Panel > Color management. Add the sRGB profile, then set it as default. Make sure Use my settings for this device is checked.
My photo which I edited is exporting to something completely different.
In what application are you viewing the exported image?
The Photos app is not color managed, and can't be trusted. The Windows Photo Viewer is color managed.
Irfanview is a free, color managed image viewer.
I was just comparing the images in lightroom for the moment. When exported i was using windows photo viewer. But the were the exact same.
It looks to me like you are running into the noise display problem. Your image is very noisy and when it is downscaled for display on a low resolution display, Develop is not accurate and tends to overdo apparent sharpness but what you are seeing is fake detail due to unrealistically large noise. Due to the way it works, Develop cannot accurately preview noise reduction and sharpening at zoomed-out views. Library is more accurate as what it does is render the image at full size and then downscales which tends to lower the noise but decrease microsharpness in the preview. You should compare the two at 1:1 zoom. At that scale Library and Develop should be identical. If they are not, you have a bad display profile.
P.S. is the image meant to be this washed out and dark? it looks like there was a curve adjustment dialed in that raises the black level to a dark grey instead of black and washes out the image and a too low exposure. This might be a stylistic choice or some present but just wandering.
What you're telling me is that Lightroom is a totally garbage editor that cannot accurately show me the edits I've applied to photos? This is not true. I've edited plenty of photo's and never ran into an issue with sharpness/noise. I'm looking for a technical solution/reason for this happening. I checked them both at the same scale. Please read what i said. Lightroom is coulour controlled.
Have you ran into these issues? I dont believe you really have. Thanks for trying to answer.
Lightroom uses a different color space in Library vs Develop modules, your critical analysis of an image should be done in Develop mode, 1:1.
You may not notice it on many many images, but they are different.
(you can use Google and search on"lightroom colorspace library vs develop"
This is an extremely common issue actually. it only shows up on very noisy images with very strong sharpening and/or noise reduction settings. This is common to all non-destructive raw editors and is done to make sure the editing process does not become glacially slow. Normally you won't notice it but you will see this on noisy images and when you are previewing on a low-resolution display (i.e. non-retina or hiDPI display). People that do star photography often run into this issue. Can you show us your detail settings?
P.S. there are times when differences in tone and color between Develop and Library are actually due to a bad monitor profile installed in the operating system. Recalibrating using good calibration hardware is the only solution for that.
Jao is quite right that Lightroom's Library module DOES NOT display noise reduction or sharpening correctly. In fact, even in Develop to see it correctly you have to be a 1:1. There's even a warning exclamation that shows if the Detail window is closed in the Detail panel. Hovering over this gives a message that says "For a more accurate preview, zoom the preview size to 100% or larger when adjusting the controls in this panel"