
Main difference from a visitors point of view is that one is about 10 times larger than the other, so lots more dogs. but usually over several days, so you have to check which day your favourite breed is scheduled.
From a participants point of view is that only at championship shows can challenge certificates be won that go towards making a dog a champion.
It gets even more complicated as most championship shows do not have CC's (challenge certificates) for all breeds. The Kennel Club rations these certificates and only allows a certain number to be competed for in a year, One is awarded to the best of each sex, though in some rarer breeds there is just one for the Best of Breed.
My own breed is not numerically strong so we have 19 sets of CC's to compete for. Two sets are at breed club shows, so that means 17 sets available, and there are over 30 all breed championship shows, so quite a few dhows don't have CC's for my breed, and some don't even have classes for my breed.
Not all breeds in the UK have champion status, so can only compete for the class awards ans best of each sex and Best of Breed.