The difference between the Develop and Library modules can be a couple of thing.
A corrupted monitor profile.
The Preview file the Library module uses to display images isn't being updated.
As for your export make sure you don't have Original selected in the import dialog window. That option exports the Original images with no LR edits.
Screen shots help a lot. So try posting some.
The Library uses previews. The Develop module uses data from the Camera Raw cache.
After editing in Develop you may need to refresh previews.
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As both Library & Develop Modules use different color spaces, that is the reason you are seeing a color difference in your images. For more details, you can refer to this article Common questions asked about Color in Lightroom CC
As both Library & Develop Modules use different color spaces, that is the reason you are seeing a color difference in your images.
There may be a difference, but you can't see it. Anything you see on screen is already clipped to sRGB on a standard monitor, and Adobe RGB on a wide gamut one. ProPhoto and Adobe RGB will appear identical on screen. Why an official Adobe article should say otherwise, is a bit of a mystery. It must have slipped through QC.
Either it's a defective monitor profile, or the preview doesn't update.
Here is the answer for Windows 10. With Picture.
1. Control Panel
2. Color Management
3. Identify your monitors
4. Select Monitor
5. Click on "Use my Settings for this Device"
6. Select sRGB IEC.. etc
7. Click button "Set as Default Profile"
9 ReStart computer.
10. Check the result in LR.
Worked for me... was driving me crazy. I had this fixed, but then reloaded win 10 with clean install. Have been fixing things for 6 weeks...