Where is the line drawn between 2D platformer and 2D fighter?

I can be considered a casual gamer, so bear with me if this isn't one of the deeper discussions on this subreddit. I was reading some interesting discussion on another post about a spectrum between the two categories. Outside of playing Mortal Kombat at my local pizza shop and playing Melee with my cousins, I tend not to play fighters, so I guess I don't understand the category so well. The major differences that I have noticed with my limited experience are as follows.

• enemies take more than one hit to kill
• your moveset is based more on button combinations than on power-ups
• your entire moveset is available from the start, with the exception of finishing moves and the like
• generally has a wide array of characters to choose from
• gameplay occurs on a flat surface, typically with no raised platforms, obstacles, or environmental hazards
• commonly has multiplayer mode and competitive aspects, allowing for tournaments

In the discussion linked above, a comment describes the Smash Bros series as being "90%" fighter, 10% platformer". This would presumably be because of the wide use of powerups and the fact that the stages can have raised platforms, obstacles, and occasionally environmental hazards. What other factors are important in fighting games that differentiate them from platformers?