The "sequel" to Flying Shark wasn't exactly the same kind of shooter as its predecessor. The gameplay is much closer to Twin Cobra than Flying Shark.
Fire Shark is a feast of weapons that almost fills the entire screen (when you've picked up enough power-pellets, that is!) which is almost opposite of Flying Shark where your best shot was a small spread of bullets. As in Twin Cobra, you can play two players at the same time, and you start at the point where you got hit instead of a bit back.
The Japanese version, Same! Same! Same! (Shark! Shark! Shark!) is different, like Kyukyoku Tiger you can only play one player at a time and when you get hit you start over a bit behind where you left off.
The music, created by Masanory Yuge who later created the music for Tatsujin Oh, is quite appealing, but unfortunately Toaplan decided to put the music code and data of the arcade version in a protected MCU (a chip with a bit of ROM, a bit of RAM and a CPU) so there is currently no way to play the game with the original sound in emulators.
SEGA Genesis was blessed with a conversion of this game, you can listen to a version of the music in that game which is a good conversion and uses basically the same music code as the arcade game.