Bose-Einstein Condensate is also known as the fifth state of matter. Indian scientist Satyendra Nath Bose is credited for its discovery with significant contribution from Albert Einstein as well. The particles of this state are called bosons. These bosons are subatomic particles with integral spins i.e., 0, 1, 2 and so on. It is formed by cooling a gas of extremely low density to very low temperatures. Because of this super low temperature, the bosons come very close to each other.
Higgs Boson on the other hand, belongs to the category of bosons but it has no integral spin and no electric charge. The Higgs Boson particle is a massive subatomic particle predicted by the Standard model of particle physics and is postulated to interact with other particles in such a way that it imparts mass to them.