Star Trek is now on several streaming services like Netflix and Amazon Prime Instant. The catch is there are different versions on each streaming service. For example, Netflix has the original version of Star Trek: The Next Generation in standard definition (SD). Amazon Prime Instant has Star Trek: The Next Generation in a re-mastered version in high definition (HD).
This is not unusual, because often the same movie on each of the services is different. One service will have a Directors Cut, one will have the Original, while a third will have an extended format.
So if you really want classic Star Trek as close to the way it was when it first aired, you will want to check out Netflix. If you want to see re-mastered special effects, make sure to check out Amazon Instant.
If you are wondering why different versions of a movie or show end up on different streaming services the simple answer is money. Content owners can charge Netflix for the original SD version, and sell the re-mastered HD version to Amazon. This allows the content owner to double their profits.
Star Wars gives us the classic example. Some fans want the true theatrical original versions. While viewers really enjoy the Special Editions. Disney could make millions offering one version on Netflix and a different version on Amazon.
In short, it comes down to money and why having subscriptions to multiple services can be beneficial.