Mechanic wise, they are not really any different in my opinion. They may deal less damage and may or may not have the high yield effect, but they have the same basic function. They both have fuel, an engine, a warhead, and a guidance system. The main difference ‘lore’ wise might be that the photon torpedo might have a small shielding unit built in, for the express purpose of making sure that a ship firing a minimal power wide-area attack with a weapons array won’t prematurely detonate a torpedo.
As for penetrating an enemies shields, there are a few episodes where it was mainly plot focus that allowed that to happen. Arguably, if you manage to find the correct shield modulation for the enemy ship, you can make it through their shields. However, if you manage to do that with a shuttle, it would be better to simply relay the info to your main ship and allow them to fire away and bypass the enemy shields in the first place with the weapon attacks. (Like the Duras sisters did in Generations.)
If that were truly the case, then they would also turn away torpedoes. Again, I think this might be part of the built-in components of a torpedo. (One of the reasons why they glow.) The shielding and other components work together with the propulsion unit to thwart and confuse the ship’s deflector shields in order to get close enough. Granted, mechanic wise, this is all kind of built into the task to hit the target. If a missile doesn’t have the same components, or quality of components, raise the difficulty to hit.
As for firing multiple shots to destroy 16 missiles? For one, each time you fire (unless you have independent phaser power supply talent) it costs your ship 1 point of energy. If your ship has enough energy to make 16 shots in one turn, use a different tactic to avoid the 16 missiles. 
That said, weapon arrays (not banks or cannons, but arrays) have the option of using an area attack. Before firing, specify you want to fire an area attack, and then for each effect rolled, you can hit an additional target within close range of the initial target (targets in contact with the target are automatically affected). So, a ship firing at the missiles (best estimate of difficulty being 2 for energy weapon, +1 for small target, +0 for medium range) would get to hit 1 missile, plus 1 additional missile for each effect rolled, costing 1 energy. That one attack would take the action of one player.
However, missiles, like torpedoes, would probably be fast-moving targets, and hit in the same ‘action’ that they are fired. So unless there is more than one player on the ship holding or readying their action to use the phasers as point-defense weaponry, those 16 missiles would hit at the same time they are launched, and would probably use the same rules as the ‘spread’ for torpedoes.