Are clathrates and interstitial compounds the same thing?
Clathrate compound :


  A clathrate is a chemical substance consisting of a lattice that traps or contains molecules. The word clathrate is derived from the Latin clathratus (clatratus), meaning ‘with bars, latticed’. Traditionally, clathrate compounds are polymeric and completely envelop the guest molecule, but in modern usage clathrates also include host–guest complexes and inclusion compounds. According to IUPAC, clathrates are inclusion compounds "in which the guest molecule is in a cage formed by the host molecule or by a lattice of host molecules."


The famous is the methane in ice clathrate $\ce{4 CH4 \cdot 23 H2O}$
Another case are clathrates of noble gases, found in hunting for noble gas compounds.

Many clathrates are stable just at low temperatures and/or high pressures.

Interstitial compound :


  An interstitial compound, or interstitial alloy, is a compound that is formed when an atom with a small enough radius sits in an interstitial “hole” in a metal lattice. Examples of small atoms are hydrogen, boron, carbon and nitrogen. The compounds are industrially important. 




So in some loose sense, the former has more or less stable non metallic lattice, the latter has stable, metallic lattice.