At a very rough level, a triathlon bike will have much more emphasis on having good aerodynamics, which is obtained to some extent at the expense of some additional weight. This is due to the fact that most triathlon bike courses will have limited hill-climbing, and are therefore more speed-oriented, where better aero really helps. ("Triathlon" bikes are really time-trial bikes, for the most part.)
In addition to using tubing that is more aerodynamic (flattened, blade-like down tubes, for example), you will also see such aero "tricks" as enclosed or hidden cabling, "carved out" seat tubes where the front of the rear wheel is really tucked into the back of the seat tube, brake locations that get them more out of the air flow (especially rear brakes in unusual locations), etc.
In terms of geometry, dedicated time-trial or trathlon bikes will have full-time aero bars, and not just clip-ons. Going along with the aero-bar riding position, the seat tube angle is significantly steeper than on a road bike - 76 or even 78 degrees, versus 72-73 degrees for a typical road bike. (Some multi-use bikes will have reversible seat posts, to allow changing the seat-tube angle.)
All of these aero improvements add a bit of weight (especially true in the case of aero wheels), so whereas a high-end road bike will be under 15 lbs, a comparably equipped and priced triathlon/TT bike might be a couple of pounds heavier.
Some road bikes are starting to incorporate some aero elements, such as blade-shape downtubes, more aero forks, etc. Felt and Cervelo have been doing this with some models, and the Ridley Noah has a bunch of neat little aero features, including slotted forks and seat stays, intended to produce better airflow.