Yes.

From Wikipedia:

Plutonium is identified as either weapons-grade, fuel-grade, or reactor-grade based on the percentage of 240Pu that it contains. Weapons-grade plutonium contains less than 7% 240Pu. Fuel-grade plutonium contains 7%–19%, and power reactor-grade contains 19% or more 240Pu. Supergrade plutonium, with less than 4% of 240Pu, is used in United States Navy weapons stored near ship and submarine crews, due to its lower radioactivity.

Weapon Grade Plutonium has lower concentration because Plutonium has a high rate of spontaneous decay which means it leads to issues with detonations in bombs.

Yes, actually. They're both different mixes of plutonium isotopes. Iirc reactor grade plutonium is far more stable than weapons grade (because blowing up is less desirable for reactors than bombs), and has some different properties when used.

Yes, "weapons grade" has a higher purity being almost entirely made of fissile isotope Pu-239

"Reactor grade" has a greater variety of isotopes.

The functional difference is that the higher purity is required to make nuclear bombs, hence "weapons grade." Purity was a significant hurdle in nuclear arms development and one if the reasons the US got the bomb before Germany or the USSR which both struggled to get sufficient purity.