The Rotate bar under the Crop & Straighten tool is used to rotate the image the way you like. For example when you were taking a landscape photo of the sand, sea, and sky, you didn't place the horizon in a perfect horizontal line and you want to fix that. You want to make the horizon perfectly horizontal so you can use the rotate bar under the Crop & Straighten tool.

The one under Lens correction is responsible to correct distortion caused by the lens manufacturing. In the profile tab you can select the manufacturer of your lens and an automatic profile (fixes) will be applied to your photo (if Lightroom has your lens profile). Note that the sliders in the Manual tab are used to give you more control to do further fine-tuning.

Exact differences are:

The Rotate bar under the Crop & Straighten tool is used to rotate the photo. Using the slider you can go from -45 to 45. You can rotate the photo clockwise or anti clockwise in 90-degrees increments. The axis of rotation is the center of the crop rectangle.

The Rotate bar under Lens Correction is used to correct camera tilt. Uses the center of the original, uncropped photo as the axis of rotation.

Please check Adobe Photoshop Lightroom 4 Guide for both here and here