However, one of them is way cheaper than the other. Which one can I trust?
Those are two different official Disney sites and are for purchasing tickets for two very different parks:
Disneyland is in Anaheim, California and opened in 1955.
Walt Disney World is in Orlando, Florida and opened in 1971.
Those are both official Disney sites, but the tickets are for two different Disney Resorts, Disneyland, which is located in Anaheim, California, and Disney World, which is located in Orlando, Florida.
There are many options for tickets in both complexes, but typically tickets either allow access to one park per day (the cheaper option), or are "park-hopper" tickets that allow switching between parks within a day. Obviously for one day tickets the former is equivalent to buying a ticket to a single park.
Is by far the larger resort, and includes the Magic Kingdom Park, the Epcot centre, Hollywood Studios, the Animal Kingdom Park and the Water Park.
Includes Disneyland Park and Disney California Adventure Park. It most closely resembles the Magic Kingdom part of Disney World though there are several differences.
From what I saw the prices are not all that different. At Orlando $97, CA $85. Keep in mind that Orlando has four different (main) parks: Animal Kingdom, Hollywood Studios, Magic Kingdom, and Epcot. There are also water parks on site that also have separate entrance fees. Entrance into each varies in prices so the $97 is just an estimate. Passes that allow someone to "park hop" are more expensive than passes to that park for the day.
A vacation to the Orlando theme parks is anything but cheap. There are ways to save money but it is still pretty expensive.
Both sites are very trustworthy in that they are Disney owned and operated. If you call them they will make a nice package for you to enjoy your stay. This would include meal plans, stays on property, and special tours.
For one of my wife's birthdays we did a special guided tour of Animal Kingdom that she still talks about to this day. It was about 4 years ago. We've also SCUBA dove the Epcot aquarium, but you have to be a certified diver to do so. It was a bit of a high price, $170 each, but it was about half the price of doing the same at the Atlanta aquarium.