Why do some pilots call a go-around an 'overshoot'?
Looking at the Glossary for Pilots and Air Traffic Services Personnel (TP 11958E) at the Government of Canada web site, the definitions of overshoot and go-around are 


  overshoot
  
  (1) To pass beyond the limit of the runway or landing field when
  trying to land.
  
  Fr: dépasser
  
  (2) Other expression for: go-around


and 


  “Go around”
  
  An expression used in radiocommunications to instruct a pilot to
  abandon an approach or landing.
  
  Fr: « Remettez les gaz »
  
  go-around
  
  The procedure followed by a pilot who decides to abandon an approach
  or landing.
  
  Fr: remise des gaz


Plus, looking at various Flight Test Guides listed at the Canadian Government Air Transportation site it appears that pilots in Canadian flight schools are taught "overshoot" procedures for missed approaches (vice go-around).

Seeing as you were watching a reality TV show dealing with Canadian pilots, it is not surprising they use the terminology they were most likely taught in flight school (in Canada).