The Inquisition punished the heretics that they would find in ways that were not allowed before. Before, when the people found heretics they would punish them lightly, but the Inquisition would now punish the heretics by death, hanging, or the like. The Inquisition would not try to correct the individuals, but to scare the public into submission.
In 1484, the Inquisition was sent to eliminate magicians and witches, for citizens were blaming certain people for bad weather, no crops and many other natural calamities. The Inquisition would punish those who claimed to be Christians, but who did not teach the teachings of the Holy Catholic Church. The Inquisition totally ignored punishing those of different religions.
In 1478, the Spanish Inquisition was started, of which was not under the crown or the church. Ferdinand and Isabella outlawed Islam and Judaism, and in 1492, all the Jews and Muslims were expelled. Although some Jews fled to Portugal, they also were persecuted.
Soon, the Catholic Church approved of certain heretical philosophers and let the Inquisition punish those who spoke of the true gospel.
The Inquisition was a ruthless force that was started by the HRE. I think that it would do better to be sure that their subjects were truly what the Inquisition thought they were.