V is made for exercise and training, while VP is mainly for training and competition.
There are probably many who are familiar with the old V-series with grip wax. Here you will find, among other things, the classic Blue Extra. These are products that work just as well today - especially for exercise and training, but the cold variants are also used in competitions.
VP is Swix's series of grip wax developed especially with competitions in mind and has been used to win cross-country skiing all the way up to the World Cup level. VP contains better and more expensive raw materials that, among other things, optimize the anti-icing properties.