The exploding crate is a combination of two popular gaming tropes - crates and explosive barrels.
Explosive crates, unlike exploding barrels, will usually be completely immovable. The exploding crate will usually be differentiated from its fellow crates by its color, or some type of visible warning marker. Explosive crates are a viable game-design alternative when the explosive barrels gameplay mechanics are needed, but having barrels in the gameplay environment makes no sense - explosive crates are a common enough occurrence in military bases and armories.
One major difference between explosive crates and explosive barrels is that explosive crates will often be volatile enough to explode when stepped or jumped upon, whereas barrels will usually only react to gunfire or intentional melee violence. This mechanic is most closely associated with the game that first popularized the exploding crates, Crash Bandicoot.