One can discern roughly three categories: Modern, Space and Fantasy/Weird shooters. Modern shooters are just that: a terrorist organisation is threatening the world and it befalls to the heroes in their F16s or MIGs to set things right once again!
Space follows the same concept, except this time it's those nasty aliens that threaten humankind, and it befalls to the heroes in their spaceships to, once again, set things right.
The Fantasy genre is by far the most interesting: there is one game where you're racing in a fantasy-style race, or you have to battle your way through Buddhist monsters!
There are some similarities that all schmups share. For instance, there are the power-ups. You shoot down a slightly larger version of the planes that fly around, and something falls out (often a little grey bomb with the letter 'P' on it -- Toaplan made the initial sprits for this and everybody stole those it seems). You fly over that, and suddenly you spray more bullets around! I can't figure out how that works: how could you instantly fit another machine gun on your plane? Or, if the gun had been fitted all along, why not use it from the start?
Then there are the Bombs. Sometimes, a black bomb-shaped sprite falls out of a plane, with a 'B' on it. You fly over these, and you pick 'em up to be used later against the level boss. That makes slightly more sense. But why don't they use their bombs against you?
The enemies? Well, the basic planes are nothing to worry about. Even though you are equiped with roughly the same type of fighter plane, there is a vast difference in firepower for some unknown reason. While your plane is capable of streaming death from multiple machine gun nozzles, complemented by, say, a battery of lasers, missles and/or small planes that follow your lead, your enemies can fire only a single bullet. A bullet that travels slower than they do. Why are we afraid of this attacker again!? Oh right, they have the numerical advantage: there's scores and scores of the generic planes (and the fighter pilots to fly them and the support staff to keep them operational), while there is only one or two of the good guys. Seriously, I understand that you choose quality over quantity, but isn't this a bit overly optimistic?
There will be scores of tanks, and often you can shoot those with the same bullets as you use for the planes -- I guess these bullets are sheets of metal a few miles high (remember, you see the action from up above) or something. How that would work out logistically, I don't know. In return, the tanks (and sometimes battleships) don't have any problem hitting you from that distance.
At least one level boss will be a tank that rides on train tracks. Why would you build such a contraption? It's hardly mobile, and all your enemies have to do is avoid the stretch of track that you're currently on, and your whole monster tank will be completely useless. It's not like you could go in pursuit of them if they leave the immediate area of the tracks.
For the rest, the law of preservation of firepower is in full effect. The enemies at the start of the game are complete pushovers, while the enemies later in the game are really hard to beat. I understand you want to have a few elite pilots to guard your home fortress, but why send completely useless pilots to strike against the designated targets? Why not send a competent force to deal with your objectives?
Really, schmups just make no sense. I just hope no aliens pull a Last Starfighter on us, because the 'pilots' so trained would be completely useless because of their unrealistic expectations of the battlefield.