In a lot of cases, saying you've "basically" finished a game if all you have left to do is defeat the final boss would be like saying you "basically" had sex because you engaged in a deep, passionate kiss with your significant other. This especially holds true in games without saving and in games with multiple separate bosses that could each be considered final. See: DoDonPachi, which has three final bosses (Hachi at the end of the first loop, Hachi at the end of the second loop, Hibachi after the second Hachi fight).
In games with loops, when you finish the game, you get to continue from a more difficult version of the beginning. It's not always that simple, however; to continue using DoDonPachi as an example, you must fulfill a special condition (such as clearing the first loop on a single credit or having a score of fifty million or better after Hachi) to be allowed to enter the second loop. Also, in Gunbird 2, the first stage of the second loop is whichever stage the player didn't go through in the first loop. (Not to be confused with the loops in Capcom's 194X series or Sonic the Hedgehog loops.)
Hibachi is what would be considered a true last boss; that is, it's a special boss, usually obscenely difficult and appearing immediately after the final boss, that often must be defeated for the player to see the true ending of the game. This often conflicts with Lizard Dude's consideration of beating the game as seeing the end credits, but it's closer to that than it is to hundred-percenting the game. True last bosses differ from optional bosses (such as the Phantom in Kingdom Hearts or the Countess in Diablo II) in that they aren't optional if you meet the requirements to fight them. Crazy Hand and Giga Bowser in Super Smash Bros. Melee could also be considered as true last bosses, I suppose.
A BAD END is when a game has multiple endings and you get a bad one. Fate/stay night and other visual novels have numerous BAD ENDs (which are labeled as such or as DEAD ENDs). Losing to Lavos at most points in Chrono Trigger triggers a BAD END. Not fulfilling a certain condition when fighting the "final" boss in many Castlevania games results in a BAD END. (Failing to trigger the second loop in DoDonPachi does not result in a BAD END, but instead a rather dull and boring end. Also, a BAD END is usually different from a standard game over in that you've still technically finished the game - just not in anything close to a good way.)
I forgot about dying referring to a game over from losing all lives rather than just losing a single life. See: Every Extend (where suicide is your only means of attack), Battle Garegga (where strategic suicide is required to keep the difficulty down and to make the most of certain scoring opportunities).
I tried to ghetto tate Ikaruga the other day (due to not being allowed to put the TV on its side), but the image didn't fit the screen properly. I tried tating the GameCube with the little screen attached (which meant putting the system itself on its side) and the image fit properly, but that screen is too small for one to be able to use it to really play shmups well.
