Wikipedia distinguishes between "Communist Parties" and "Trotskyist Parties".
It lists the SWP (USA) as a Communist Party and the SWP (UK) as a Trotskyist Party:
en.wikipedia.org/wiki/Portal:Communism
The SWP (USA) and SWP (UK) are not currently linked in any way.
I stopped trying to make sense of all the different Far Left Parties and Factions over 40 years ago. A lot of them were little more than three men and a dog so it wasn't worth the effort.
However, there does seem to be a split between (some of) the Parties that are Communist and the Trotskyites (eg. SWP UK) in terms of recognition of material reality and support for women's rights. The SWP (UK) also has a disgusting history of sexual exploitation of women.
SWP (UK) - Internal crisis in 2013–2014 over allegations of rape
en.wikipedia.org/wiki/Socialist_Workers_Party_(UK)#Internal_crisis_in_2013%E2%80%932014_over_allegations_of_rape