Do you mean catchment?
Or do you simply mean living close enough to fall within the greatest difference offered?
Catchment should be clearly published each year (and only changed after public consultation, though it can be easy to miss that consultation is going on).
When there are catchments, and the criteria (typically ) run 'LAC/SEN, catchment siblings, all others in catchment,non-catchment siblings, all others' it is very important to know which category you will be in when you are deciding your preferences. (Though of course being in catchment is not always enough - it settles which category you are in but if, for example, the 'other catchment children' is the tiebreak category, you can still miss out if all places are filled by those living closer)
Unfortunately, school staff (who should know better) do not always describe admissions properly, and may confusingly misuse terms.
It sounds as if there may be no catchments in your area, and that where you currently live is not close enough to qualify you for any offer (on offers day - greatest distance by admissions day - after waiting list movement - can be larger but does not have to be published).
The uncertainties of getting a place you like better at another school (now that all places have been offered) have been described by previous posters. You are lucky that you have another option (private school place lined up, or likely vacancies in an acceptable school nearby) and I hope it works out.