Second, TPS are geared more towards tactical play because the third person camera allows you to walk up to a surface unseen and "look around" for your target before you stick your head out to fight.
A mechanic which I actually dislike in TPS. You should have to stick out your head (like the GTA IV cover system allows you to do) to see what is around the corner. As long as you do, everything happens in real time. But when you get your head back behind cover, everything goes grayscale and you can only see people's positions like in Splinter Cell: Conviction after you've gone stealthy again.
Nothing breaks the immersion of a game more than third person view. The first time I meleed someone in Monday Night Combat and had the view pop out and show the animation in 3rd person I puked a little in my mouth. First person view is the greatest thing in gaming since mouse look.
First person = You are the character
Third person = You are puppeteering a puppet
Well, I am on the other side of the fence. FPS usually make me feel like a gun hovering around. TPS make me feel like I am playing a character.
Your definition of Third Person is quite accurate, though, because it's like being a child playing with action figures. As a child, you'd imagine you are the action figure. That's how TPSs work for me and that's how they increase my gaming experience over FPSs.