DLR and WDW do share a number of rides, but it's worth noting that even rides with the same names are not necessarily the same at both parks. There are actually very few rides that are identical (or nearly identical) in both resorts. The ones that come to mind are Star Tours (the queue is very different), Little Mermaid (subtle differences and a very different queue), TSMM (queue different), and It's Tough to be a Bug.
Space Mountain, It's Small World, Pirates of the Caribbean, Haunted Mansion, Buzz Lightyear Astro Blasters, Jungle Cruise, Splash Mountain, Big Thunder Mountain Railroad*, and Soarin') are at both resorts, but the DLR and WDW versions are not identical. I would still try to ride most of these to see the differences. For some, it's a fairly minor difference (e.g., Soarin' ends in DL rather than Epcot), while others are pretty different (e.g., Space). (*The Big Thunder track is almost a mirror image of the one at the MK, so if you're used to going left, it'll go right!)
Other attractions are completely unique to DLR. The ones that come to mind are Roger Rabbit's Cartoon Spin, most-everything in Fantasyland (e.g., Matterhorn, Mr. Toad, Snow White, etc.), Indy Jones, everything in Carsland, Screamin', Monster's Inc., GotG: Mission Breakout (opening Memorial Day weekend), Frozen Live at the Hyperion. There are also a number of rides that are similar to something in WDW, but have a different theme (e.g., Goofy's Sky School, GRR).
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