Like many other huge, multi-national corporations, Disney consists of many different companies under one brand.
Disney Cruise Line is actually a separate company from Disney Parks and Resorts.
Disney Cruise Lines Inc. is based in Kissimmee, Florida while Disney Parks and Resorts Inc. is based in Lake Buena Vista, Florida. The Walt Disney Company is headquartered in Burbank, CA.
The reservations systems are completely separate. They don't even link to each other and what you book in one place isn't visible to what you book in another. Even the shuttle services are treated separately.
When you are on the ship or in the parks, you are likely experiencing entertainment options from a variety of Disney companies. Walt Disney Imagineering operates Walt Disney Entertainment and Walt Disney Theatrical, which takes care of all the live entertainment, then there are all the movie companies (Touchstone, Lucas Film, ILM, Pixar, Marvel, WD Animation, etc.) followed by the ABC properties.
I could have some of this wrong and it's far from an exhaustive list, but most of the time when we think Disney, we are actually referring to a complex web of companies, many privately held by the Walt Disney Company. That said, they have their own profit/loss to maintain and often have the autonomy to decide how to operate, so long a they follow the core brand principles. That means choosing their own technology solutions for their reservations systems.