you are both right and wrong.. Las Vegas Strip and McCarren Airport are technically Paradise, Nevada.. but its not really a city.. its called an "unincorporated town" basically governed by its own county/laws (pretty much a loop hole for vegas to be set up). But if you are flying into McCarren Airport which is technically Paradise, Nevada - its still classified as Las Vegas (LAS for airport code/flights)
Unincorporated towns in Nevada - Wikipedia, the free encyclopedia
its because of how the hotels are set up (revenue sharing with the city)
dont quote me on this but with the loop hole I think the hotels only have to share revenue with what is classified as "Paradise, Nevada" (200,000 residents) instead of the entire city of Las Vegas (600,000 population).
Probably some crooked politician set it up this way to line their pockets from the hotels