They're NOT the same. (Although what's in a name).
The FEO is the Firearms Enquiry Officer. He/she is the person who gets your application, makes all the enquiries, does the 'phone calls, visits you, checks your security, puts it all together with your application and submits it with a recommendation to:
The Firearms Licencing Officer. He/she is the person who looks at your application and decides whether to allow it or not and with what conditions.
It's true that the Chief Constable has the responsibility to grant/refuse certificates and in theory at least, the buck stops there. In practice, this is delegated to one of the other chief officers (an assistant chief constable or perhaps deputy chief constable, depending on the force's organisation). Who, in turn will delegate it to the Superintendent/Chief superintendent or sometimes civilian head of department, who in turn delegates it to the Firearms Licencing Officer. The Firearms Licencing Officer, in effect makes all the day-to-day decisions, based on the law, Home Office Guidance and force policy. Those further up the pyramid will usually only be involved in general policy decisions and if the poo hits the fan, not usually in particular cases of whether to grant/renew or not.
This, of course is an indication of why policing costs so much to the poor taxpayer these days. There are, despite successive cuts to police budgets, still people in police headquarters all over the country sitting in offices who do not look out of their window in the morning, because it will leave them nothing to do after lunch. It also beggars belief that so many police areas are so behind on their licencing schedules. But that's another subject for another thread.
For evidence of this, look at your certificate. There are two signatures on it. One should be yours, which you signed when you got it, the other is the authorising Firearms Licencing Officer. Not the Chief Constable and not the Firearms Enquiry Officer.