Generally, independent schools do not expect state school children to take the common entrance exams (standard or scholarship) in year 8. Instead, they will often set their own entrance exams for such pupils which reflect the national curriculum and look for potential.
Some top (generally boys') schools set their own scholarship exams for state school pupils in year 6. These are looking for intelligence and potential, not proficiency in Latin etc! If the pupil is offered a scholarship this will generally include funding for the boy to go to a feeder prep school for two years (years 7 and 8 ) before joining the senior school in year 9 together with all the other, privately educated boys. That way the boy will not be behind the others when he starts in year 9, as he might be if he stayed in the state sector for those two years. He will also have had the chance to make friends with some of his future peers before he arrives, so he won't be the odd one out.
If your child is at an independent school already and you want to see what the difference is between the standard and scholarship papers at CE, go to this site www.iseb.co.uk/syllabus.htm
and look through the various linked syllabuses. If you read them to the end they will tell you what will be in the scholarship papers.