Why might two different chemical structures smell the same?
The molecular determinants of odor perception is a disputed area in fragrance biochemistry.  There are two basic theories: the "shape" hypothesis and the "vibrations" hypothesis.  Luca Turin is the foremost exponent of the more controversial and less widespread "vibrations" hypothesis, but he does a good job of explaining both theories in his TED talk.

According to the vibrational theory, since different functional groups have different vibrational modes, they should smell quite different.  An example from Luca's talk is a complex alcohol vs. the corresponding thiol.

According to the shape theory, molecules which have similar but not identical functional groups should smell similarly, unless the protein receptors in our nose that sense odors have very exquisite shape sensitivity, enough to perceive the very slight difference in the shape of thiol vs. an alcohol in a large otherwise identical molecule.


  Why might two different chemical structures smell the same?


According to one theory, they would smell the same if they had similar vibrational (i.e. infrared) spectra.  In 2011, PNAS published is a very intriguing result that showed this was true for fruit flies in the case of some odorants.  They changed the vibrations by isotopic substitutions, a method that should leave essentially unchanged molecule's shape and its chemical reactivity.


  So, would that make it so that two different molecules with the same functional groups would smell the same?


In my mind this is true if you believe the vibrational theory as well.  But it is harder to understand why it is true if you believe the shape theory.

Of course, the real answer may be a combination of both theories.  I'm a tepid supporter of the vibration theory myself, but I would be very interested in a chem.se answer from another expert who is less impressed with Dr. Turin's theories than me.