Technically, they are called awarding organisations (I believed OCR even refer to themselves as an 'awarding body.'). They are all regulated by a quango called Ofqual, ensuring that standards are maintained equally between the four in England. There should be no difference in rigour in the specifications offered by different awarding organisations; any slight difference in difficulty between the examination papers from different awarding organisations is accounted for in adjustments to their grade boundaries. I do not believe that there should be any discrepancy in the values of a grade awarded by any of the four awarding organisations in England, your grade 9 with Edexcel is equivalent to a grade 9 with AQA and so forth.
Exam boards are an artefact of the English education system – they only really existed in the twentieth century.