Hi
Culmstock is in Devon, and was in 1861 but it was, and is, in Wellington (Somerset) registration district. Births in Culmstock are recorded in Census returns as Culmstock, Devon
It is in Tiverton, Devon district for Census returns.
I will also post my message in Somerset, but assume that Culm Valley records are held in both Somerset and Devon records offices.
And yes it is confusing, but not as bad as Berkshire that is now Oxfordshire!
Ken