bike shorts usually have a rather large padding; if you happen to swim with them, even under your wetsuit, you'll absorb a lot of water. then on the run, they're rather cumbersome.
tri shorts, at least ours, are slim, water repellent and seamless. they'll offer you great comfort on the bike and you wont notice them while running.
some of those shorts have a compression factor as well that can help reduce muscle fatigue.