Yes. And yes on the second count. I believe Oneechanbara is considered of the same 'genre' and I believe even has some of the same devs - I know Goons were discussing who would win in a fight between the two games' protagonists, once.
Also EDF is itself the second game in a series. There was an earlier game, but it was Japan only and for the PS2. I understand it had two playable characters, one of which, the chick, had a fucking jetpack.