I guess all vets have different protocols on what vaccination to give - and I guess they all have their reasons why.
Generally puppies get three vaccinations. Their first one is generally a C3 vaccination and is given between 6-8 weeks of age, the second one is a C5 vaccination and is given between 12-14 weeks of age and the third is another C5 vaccination and is given between 16-18 weeks of age.
A puppy (older than the ages stated) or a dog with no vaccination history get two vaccinations, generally C5's which are given four weeks apart.
PLEASE NOTE THE WORD 'GENERALLY.' Like I said, all vets have different vacc protocols, I'm just giving info from where I work.