So when I switch back between library and develop module in lightroom classic my images are drastically different. The color changes and they becomes grainy. I would like to fix this but I have no idea where to begin. I attached two photos one of each module to show a example.
Sorry that you're the image in the Develop and the Library module is not matching in Lightroom Classic CC.
Which version of Lightroom Classic are you using? The latest is v 10.2
Before we start troubleshooting it, I'd recommend that you please take a look at this discussion Develop module & library module aren't matching and let us know if that helps.
You should compare at 1:1 view, which maps exactly one image pixel to exactly one screen pixel.
Screen resampling algorithms are different between the two modules. Image noise and so on can respond differently to resampling.
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You have chosen to build Embedded & sidecar previews when importing.
The embedded previews are created by the camera, and are also processed in the camera with whatever settings you have chosen. This particular preview has had noise reduction applied.
Embedded previews will be replaced by Lightroom's own previews as you work, and to replace the preview for one image, click the badge in the top left corner of the thumbnail and choose Build Standard preview or 1:1 preview.
You can also select several thumbnails, and go to Library > Previews.
In the future, please insert images directly in your posts, use the Insert Photos button in the toolbar.
Also, rather than using a camera, take proper screenshots. See https://www.take-a-screenshot.org/
Along with what the two previous two people mentioned, and another item to consider is that the Library Module uses Adobe RGB as color space and the Develop Module uses Melissa RGB (similar to ProPhoto RGB), which will cause slight color shifts depending on the images.
In this case it's definitely caused by the embedded preview.
Per, good catch!