DVD mastering software can construct those menus from the various chapters that are on the disc, including the (often animated) video effects that you describe.
You’re probably looking at the consequences of what’s called (in Blender, which is what I use), node-based compositing (rendering, materials, textures, etc.). Imagine if you will a “maze of pipes” connecting inputs, filters, and outputs such that the final image is built-up through a series of steps … in a way that can vary, for example, based on variables such as camera position. The final image(s) pop out from the output-nodes in this “factory assembly-line.”
You’re also probably looking at individual animations, and/or still frames, perhaps “filmed” separately, and then brought together into the final show through techniques like these. If the object “transforms” from a flat billboard into the depicted object, that’s an animation, or the “flat billboard” appearance could also be a visual transformation (created by an appropriate node-network, or “noodle”), which on the appropriate cue “turns off” to reveal the animated model that, in fact, has always been standing there.
These effects are quite remarkable (and fun to do), and it’s definitely one of those things that leaves your friends saying, “How’d you do that?” :bowdown: The appropriate response, of course, being “a mysterious smile.” 
