Data Space and K-Space
Just the axes. Asymmetry in the data space is possible, because the axes of data space are time. This is obvious, because acquiring one phase encoding step (filling a line in the frequency encoding direction) takes milliseconds, whereas filling k-space to have a full dataset in the phase encoding direction can take minutes. K-space axes are spatial frequency and so this matrix is symmetric. Getting from data space to k-space is a simple mathematical manipulation. You can Fourier transform either to get the image. We work with k-space and not data space because it is more instructive about what the data is and thus aids understanding.
So they're equivalent, for all intents and purposes!
What the data in k-space really is, is explored more fully in the What Is K-Space? tutorial.
Further reading on this topic:
Books: MRI The Basics p163