11X is a reporting code and not an MOS. You are put in as an 11X, sent to Benning School for Boys, Go through the first several phases of Infantry One Station Unit Training, and then part of the class--usually a smaller part--get assigned 11C and the rest are assigned 11B.
Then you complete training.
The funny thing is that 11C's get to go to more types of units and--if they reclassify to 11B later--don't have to go through an AIT again...
So, to summarize, an 11B is someone who went to Benning with an 11X and stayed with the pack and an 11C is someone who went to Benning with either an 11X or 11C and went the road less traveled.