Here's how to tell.
Could you take the newer game, switch out the sprites or character designs, make a few minor gameplay tweaks (and level redesigns, if applicable), and have a game practically identical to the old game? Then it's a clone.
Take Playstation All-Stars Battle Royale - if you switched out the Sony characters for Nintendo characters and switched the damage meter to percentage rather than HP, you'd think you were playing Smash Bros. That makes it a clone.
Note that implementation issues aren't factored in. A clone can be far better or far worse than the original in terms of gaming experience. "Clone" isn't necessarily a negative term, although many will use it negatively. As an example, many would probably call the original Metroid a Kid Icarus clone.