Unincorporated company

I am confused because a line in BPP suggests that even unincorporated firms need to pay CT. here's the line: "A company is any corporate body (limited or unlimited) or unincorporated association, eg sports club. And Companies must pay corporation tax on their taxable total profits for each accounting period. " How is this possible pvt. company would mean self-employed business and there are different rules for that as far as my understanding is concerned. Am i going awry somewhere, sir? if yes can you help me out

or perhaps it is like both have to pay CT, regardless of whether they are listed or not, just that in case of private firms CYB rule will be followed and in case of listed companies AP rule will be followed

No. ALL companies pay CT irrespective of size. In addition as the BPP note says - an unincorporated association like a sports club does not pay income tax - income tax is charged on individuals and HMRC are not going to charge every member of the club! - so instead the club itself should there be any profits will pay CT on such taxable profits