The last time I was in London. the Circle line was still just a circle, without the Hammersmith extension. On our trip this year, we will be staying in Notting Hill, near the Westbourne Park stop on the extension. It is not clear to me how the trains run once the extension reaches the circle.
If we get on there, are there two different trains that will head toward the circle, and then split at Edgeware Rd., one going clockwise and the other going counter-clockwise? Or, for example, if we wanted to head towards South Kensington, would we have to get off at Edgeware, and then get on another Circle train that goes counter-clockwise.
You would just go to Notting Hill Gate Station and take the Circle Line via Victoria 3 stops to South Kensington.
The CityMapper will give you all the options for any journey.
You could go to Paddington and get the Circle Line via Victoria but I suspect that would take longer.