Which one is being used by the school, and which by the county council?
I would have thought the number should be the same (assuming they're talking about the same
year of entry).
The current Codes of Practice refer to an 'Admission Number' (which means the published Admission Number).
A decade ago the term used to be 'Standard Number'. This changed following the Education Act 2002:
The Education Act 2002 removed the need for schools to define their capacity by
means of ‘standard numbers’ which could only be changed by publishing statutory
proposals – instead, admission authorities will rely on a published admission
number determined following local consultation. This number should relate,
though, to the assessed capacity of the school and to sensible organisation of
children and classes within the school. [Admissions Code 2003]
The assessment of a school's capacity does include something called the "Indicated Admission Number" - one of the factors to be taken into account when deciding on the published Admission Number.