Is there a difference between receiving a copyright registration from the LOC and being granted a copyright?
There aren't two separate things in US law. I think you're confusing the terms, which is understandable with just about every legal term.
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I generally do not use the wording "granted a copyright", but it sounds like this may be the same thing as a "copyright registration" granted by the U.S. Copyright Office. Remember, in the U.S., a creator of an original work of authorship owns the copyright in his/her work as soon as it is fixed in a tangible form of expression. There is no requirement for copyright registration as copyright protection is secured once the work is created and fixed for the first time. However, copyright registration provides certain advantages to the copyright owner, including the right to sue for infringement, and the potential for obtaining statutory damages and attorneys fees if successful in a court action.