This is caused by the Library display being done from a jpeg preview that is scaled down to the display size. Scaling down makes it slightly more blurry. In the Develop display, the image is displayed form the actual raw file that is subsampled to the display size and it applies a bit of sharpening to approximate the effect of output sharpening. So in effect it is simply a different way of scaling to the display resolution. In Both modules you CANNOT judge the image sharpness while looking at the image at Fill or Fit. This is because your display is a low resolution device and the program has to scale down your image to the display resolution which necesarily introduces bias based on the algorithm used. The ONLY way you can judge sharpness of a digital image is if you zoom to 1:1 (or higher). You will see that if you zoom to 1:1 and toggle between develop and library, the sharpness will be identical. Also, if you use high resolution displays (e.g. retina or HiDPI displays), this problem is mitigated and you won't be able to see much difference.
The sharpness of actual output files will depend on many factors such as whether you scale and if you scale whether you apply output sharpening in the export. You should only apply output sharpening if you scale down an image but typically always do so if you scale down.