I can see shooter as a cover for all of them but I tend to think of them in sub-genres. Stating rail shooter tends to indicate that it will be an into-the-screen scrolling shooting game. Shooter by itself makes me think of any of the traditional side/vertical scrolling games. Twin stick shooter is an overhead that can be limited to one screen but is often more free-roaming than other shooters. For me the bigger issue is that a lot of people nowadays tend to use the term shooter to identify FPS/TPS games.
After Burner Climax was pretty cool, S&P2 was really good but maybe too long, and I liked Child of Eden.
DoDonPachi Resurrection
Jamestown
Ikaruga HD
Mushihime Futari
Sine Mora
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