Exhibition: put chicken in cage and the judge will rank it according to the apa standard of perfection against the other birds starting with birds of similar breed and variety, if it comes out at the top of its variety then it will be judged against the other varieties of the breed, if its still on top then its judged against the other breeds. In a large show the average person is lucky if they rank in the top 5 of their variety depending on the # of birds.
Showmanship: in my neck of the woods its usually only the kids who do it, take the bird out of the cage, judged on cleanliness, handling ability, knowledge of individual bird and breed sometimes other breed, general poultry knowledge, disease awareness etc.
Commercial: meat birds, often auctioned off after the show, in some areas and shows certain egg layers and mixed breeds will be accepted but this is usually not the case, most shows don't have a commercial division and it is most often seen at a meat bird only competition.
Walking the chicken i'm assuming is refering to showmanship because you do have to pose the bird in its breed specific stance, but i'v really never heard the phrase. Chickens usually don't get vaccines, they get pullorum tested, any legit show will require you to send in a negative pullorum certificate with your entry sheet. There's a huge difference between shows and fairs, fairs tend to be great places to pick up diseases and see all kinds of low quality birds, if you really want to show start going to actual chicken shows, just go to a few before entering birds or getting involved. To get a pullorum certificate you can probably google your state and the word pullorum test, its free and they send an inspector out to your house to take some blood from the birds. Also do not expect to do well if your birds are hatchery stock, go to a show (not fair) and if you decide this is something you want to do pick up a good quality breeding trio and start off from there.