Tri bike vs. TT bike

Depends if you are going by UCI vs. USAT regulations.  If so, then yes, there will be a difference between a pure TT bike and a typical tri bike.

But for all intents and purposes here, no, there is really no difference.

Some pure TT bikes use a slightly slacker seat tube angle than Tri bikes. 

Mark

And some frames marketed as "tri bikes" have much slacker head tubes than others.