What is the difference between Powerful Gear and Legendary Gear rewards?

Destiny and Destiny 2 contain the same loot hierarchy. This is:

White (Common) < Green (Uncommon) < Blue (Rare) < Purple (Legendary) < Yellow (Exotic)

There is no tier of gear called "Powerful"; as the other answers have pointed out, these "Powerful gear" rewards give you a Luminous Engram.

"Powerful gear" rewards, which are Luminous Engrams, differ from Legendary Engrams in the fact that:

• The Power of the items will be above your level, even once other items have "stopped" at 265 (more on this below)
• You receive two items from the Powerful gear reward, one of which has a high chance of being an Exotic
• Oftentimes these rewards will have Legendary Mods that give them +5 power, but not always; more often than not these are present in the Nightfall lumnious engram
• These Powerful Gear rewards are available weekly (on each character!) from a variety of weekly activities called "Milestones".
• Luminous Engrams are not "locked" at the light level they drop. Revisiting the rewards vendor who has a Luminous Engram available to give you after increasing your Power will increase the Power of the engram as well

It is worth noting that other items will not stop at 265. So far, no one is quite sure what this number is, but items will drop above 265 after a point. However, they will be stuck at 265 for quite a while until your Power becomes above 270, at which they will begin to slowly and incrementally increase in power. This likely beings around Power 276, the pattern for scaling Legendary Engrams appears to be 10 Power less than your current Power level, not factoring mods. So, if you are Power 295 and have no legendary mods installed, your Legendary Engrams will drop around 285.

Once you hit "true" Power 300 (this is Power 305 if everything is slotted with mods), engrams begin to drop in rotating patterns from vendors between 295 and 300. But that's a whole other rabbit hole.