A Multipower is a pool of points that can be assigned on the fly to a limited selection of pre-defined powers, and usually represents either a set number of frequently-used abilities/gear or a single power that can be used in different ways (often known as "tricks" or "stunts"). Some examples:
-an archer with several different types of trick arrow (Green Arrow or Hawkeye) -a gun with several different firing modes (regular bullets, grenades, flamethrower, etc.) -a wizard who knows a handful of spells which he uses repeatedly -someone who can project and control a specific type of energy for varying applications (Human Torch)
Essentially, a Multipower is a discount offered to the player for accepting a restriction on how much of his various powers he can use in a single action. The Human Torch is a classic example. He has one basic power (the ability to create and control flames) that can produce a myriad of effects. If he tried to purchase all of those effects as separate Powers, he wouldn't have any points left over to spend on his unstable molecule costume, but the character "should" have them. Worse, if you did manage to squeeze them all onto his character sheet as individual Powers, then he could conceivably activate them all on a single Phase which would make him wildly overpowered compared to, say, Spider-man, and ISN'T something the published character is capable of doing. Multipower allows Johnny to have the ability to do goofy stuff with his flames, like projecting them in different shapes or at different intensities, but he can only use one 'stunt' at a time. It's a bit more useful than a straight 12d6 Fire Blast, and it costs a bit more, so it all balances out.
A Variable Power Pool is broadly similar to a Multipower, in that it's a pool of points that can be assigned to different Powers. However, it's far more flexible, in part because the powers in the VPP don't have to be pre-defined. VPP usually represents a character with complete mastery over a broad category of power or ability. Some examples include:
- an archmage who knows every spell in the book, and routinely writes his own (Dr. Strange, Dr. Fate) - an inventor who can whip up a device to defeat an alien invasion out of the stuff in his garage (Reed Richards, MacGuyver) - a dude who is so well-prepared that he always 'just happens' to have the right tool 'for just such an occasion' (Batman) - a character who can copy other people's powers (Rogue) - a shapeshifter who can turn into almost anything (Plastic Man)
Essentially, the only limits on a VPP are: the number of points available, the imagination of the player, the special effects of the powers, the character's skill in manipulating the powers, the player's knowledge of the rules, and the GM's patience. Which means there actually are fairly sharp limits to a VPP. They tend to be more expensive than an equivalent Multipower, at least up to the point where the costs of the individual slots in the Multipower become significant (as Hyper-Man says above).
VPPs are far more complex gameplay-wise than Multipowers. Even with experienced players and GMs, a VPP can slow down the game while the player tries to concoct a brand-new power on the fly in combat, and the GM has to determine (again, on the fly) whether or not it fits the character concept, is legal, and is fair/balanced/appropriate to the setting, etc. VPPs also have the potential to derail plots and overshadow other PCs. For all these reasons, they are not recommended for inexperienced players and GMs, and some GMs just disallow them entirely. Other GMs allow VPPs, but ask players to only write up new powers during down time.
Multipowers are much less dangerous, though they do deserve to be reviewed occasionally to make sure they are built around a legitimate special effect and aren't just a fudge to get lots of combat powers for low, low rates. They're also simpler in most ways than VPPs. In most cases, if you're having trouble deciding whether a VPP or a Multipower is appropriate for a given character, my rule of thumb is, "If it CAN be built with Multipower instead of VPP, it probably SHOULD be built with Multipower instead of VPP."