66,
The 3 year certification period. is absolute.
The 6 month or 12 month option you are being quoted is from the registrar (of your choice) for surveillance (abbreviated) audits for the total certification period of 3 years.
One you have been certified, the 3 year period starts.
You have the choice of the registrar coming into your facility(ies) every 6 months or every 12 months to look at portions of your QMS to determine continued effectiveness (or not) during this 3 year period.
So, if you choose the 12 month option, the registrar will surveillance audit you for 2 consecutive years. In the 3rd year, they will audit the entire QMS again to recertify you for another 3 year period.
The frequency of the surveillance audits is entirely up to you.
Good Luck.