there's a lot of varying answers in this thread. in general there are 3 types of "enrages", if you want to sum up everything that's being mentioned.

2 of these are room-wide aoe's that pierce dragonblood and resists and take you instantly to the death state, bypassing near-death. this happens on many bosses when you fail to kill them before the enrage timer reaches 0 and is often due to insufficient dps. the other kind is when certain mechanics are not done properly, and can happen at various times throughout the encounter, depending on how the party performs. a good example of these is asura, which has an enrage timer but will also do the same room-wide aoe if he absorbs too many lifeblooms.

the third kind does not cause instant death but significantly increases the difficulty, either through a change in the attack rotation, increased boss defenses, or both. this usually results from a failure to do mechanics properly. an example of this is failing to cc the drill sergeant in nexus correctly. he gains a defensive buff and many saws begin traveling around the room. however, this enrage state can be eliminated if party members survive to the next cc phase and do it correctly. another example is fujin and raijin, where damaging aoe's are spammed often by 1 of them if the other is taken down. (interestingly enough, the twins do not enter a hard enrage after the timer ends, only spamming these aoe's which can allow for party members to continue iframing or sustaining through the damage and providing dps well after the time limit has expired)

the established MMO terminology refers to the first 2 examples as "hard enrages" and "soft enrages", respectively. running out of time and failing to kill a boss is a "hard enrage", as that is set in stone and there is nothing that players can do about it. if the boss is not dead by this time, then the party dies. failure to do mechanics properly can have 2 different outcomes. if it is an action that functions the same as a "hard enrage" (unavoidable, pierces dragonblood, immediate death state) then it is referred to as a "soft enrage". the boss may also increase in difficulty by changing its attack pattern or by gaining buffs, and it seems intuitive to call this change a "soft enrage" because it does not mean instant death for the party, but that's not what the term "soft enrage" has traditionally encompassed.