Local government is divided into three layers:
Somerset County Council covers (naturally) the whole county. Within Somerset there are now five districts.
West Somerset and Taunton District Council now covers the (previous) two districts the name suggests. Within each district there are numerous Parish Councils:

Stoke St Gregory Parish Council is one of 80 Parish Councils in the District. There is a separate tab on the navigation bar above for everything related to Stoke St Gregory PC.

Plans have been mooted, on various occasions to merge the County Council and District Councils into one or more Unitary Authorities, but for now the three tier system described above is what we have.

Somerset County Council

The division of responsibilities between County and District Councils is not always clear, but for the most part County is responsible for county-wide services such as transport networks (highways and footpaths), education and care services, waste and recycling (except for roadside collection), libraries and more.

Somerset County Council website.
Somerset County Council    
County Hall    
TA1 4DY  

Phone 0300 123 2224 Lines are open 8am to 6pm Monday and 8.30am to 5.30pm Tuesday to Friday

Somerset West and Taunton District Council

This is a very recent (1 April 2019—yes really!) merger between the previous West Somerset District Council and Taunton Deane District Council. The District Council is responsible for collecting waste and recycling —and council tax, but the chief way in which we interact with them is that they control nearly all the planning decisions within the district.

Somerset West and Taunton website.
Somerset West and Taunton Council
PO Box 866

Main offices at Deane House, Taunton and West Somerset House,
Tel 0300 304 8000 Lines opening hours 8am-6pm Mon–Fri