Animation data specified in an FBX file for a scene takes the following structure:
n Animation Takes, containing:
n Animation Layers, containing:
n Animation Channels, containing:
n Animation Curves
Animation Takes (also called Stacks internally by FBX, but nowhere else it seems) define discrete animations that you might want to play. These quite easily map to our concept of animation clips in Storyboard Designer. Unfortunately, support for defining Animation Takes in many DCC tools is somewhat limited, see the note below. You can think of a Take in the film sense, "Action! ... do stuff, do stuff, do stuff... Cut!".
Animation Layers define a set of curves that you may want to play in parallel with another layer, allowing you to essentially modulate the defined motion of another layer. An example would be a sphere moving along a path (layer 1), while bouncing up and down (layer 2). These don't really map to anything in Storyboard, we would likely just import multiple layers of animation motion into a single clip.
Even though Animation Layers have little meaning to us, they are important because they are the container for a set of channels/curves.
Animation channels define what precisely we are deforming. These map to rows in our animation timeline. An example here would be "FrontDriversSideDoor, X rotation".
Each channel as mentioned above has a set of Curves, which basically map to the ends of Animation Steps in Storyboard. The curves are defined using key frames, with a time and a value.
In reality, most DCC tools (except MotionBuilder), will require any use of layers to be baked down into a single layer, and as mentioned above (and expanded on below), multiple takes are not natively supported either.