Logging flight hours

[Puffpuffgive]

Morning,

I have two questions. I hold a UK and a Canadian PPL.

Does the CAA require you to log every flight that you fly in your pilots log?

Transport Canada and the CAA have different rules on how some flights are logged (such as Cross Country), who's rules should I follow in my pilot log book, should I record each flight twice in two pilot logs one for UK and one for Canada?

Thanks for any advice