A LinkedIn Recommendation as compared to an Academic Recommendation In what ways would a Professor's LinkedIn Recommendation differ from his Recommendation for Graduate School(Masters/PhD)?

In other words: In what was does the visibility of a Recommendation change a Professor's Recommendation?
I believe they are totally different. 


LinkedIn recommendation is more towards the visibility of student's soft/technical skills in general while the official letter of recommendation should address the student skills in a more academic/depth way.
Their audience is different. Recommendation Letter is intended to particular institute/committee while LinkedIn is more to the public general and industry recruiters in particular.
LinkedIn recommendations counts nothing for the admission committees while might have good impact on industry recruiters. 


In short: Academia:- Recommendation Letters. Industry: doesn't hurt to let your supervisor recommending you - if they do have account on LinkedIn :-)