Naturalisation: approval of citizenship vs citzenship ceremony letter

Hi all,

My Australian wife has applied for UK Citizenship via naturalisation following ILR approval after 2 x 2.5 year spouse visas.

What I'm struggling to understand is if there are separate documents/emails for the approval from Home Office and the invitation to a citizenship ceremony.
Council websites suggest they are separate and that there can be up to 3-4 months lag between them. But from looking at the Naturalisation Timeline board here it appears that there are examples of them being granted on the same date and possibly in the same document.

I'd appreciate the experience of others given there's quite a difference between waiting 3-4 months or being immediate.

Details:
Nationality: Australian
Path: Spouse visa then ILR after 5 years (2 x 2.5 year spouse visas)
Applied using UK VCAS IDV app, as had attended a centre for ILR very recently

Thanks,
James

Hi,
You typically receive just one email of approval which will have your reference number after which you need to call the council to book your citizenship ceremony. At the ceremony you get a certificate which you use to apply for your British Passport

Many thanks!