No youre not missing anything, youre spot on. They are in no way comparable. Both wolfburg and leverkusen are simply clubs situated in a city that is heavily influenced by a single company and naturally created football and other sports clubs. As you said, they are just worker clubs that have existed for a long time. In comparison redbull is a new brand that isnt even german.
There absolutely is a big difference between the two and people who call wolfburg or leverkusen plastic clubs are just clueless haters.