I think distillation and pruning are more similar as they both relies on the overparametrization and in distillation you control the prior of the student model arch.
But if the pruning could start to be efficently structured I think that at some point the two approaches could go to converge in something else. See some Deepmind early findings:

  
      

      arXiv.org
  

  
    

A Generalized Lottery Ticket Hypothesis 2

  We introduce a generalization to the lottery ticket hypothesis in which the
notion of "sparsity" is relaxed by choosing an arbitrary basis in the space of
parameters. We present evidence that the original results reported for the
canonical basis...