TT or Tri bike, which one?

I've recently fallen into time trialing. I'm riding on my Madone with clip on aero bars. It's okay for now, but I have really loved time trialing and want to get a TT bike. Is there a difference in a TT bike and a tri bike? Any suggestions as to a specific bike for me? I'm looking to spend about $2k give or take a couple hundred.

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Lemond Tete De Course
-Sram Force
Trek T1