In the Spanish and Portuguese Inquisitions, this is a distinction without a difference. Further, throughout much of the European history of the Catholic church, the distinction between the church and the executive function of the state was practically nonexistent.
I'm just saying we shouldn't get on a high horse about "death spectacles".
A lot of things in history, with regards to the negative impacts of religion, have been rather exaggerated. For instance during the Spanish Inquisition a total of ~3,000 people were put to death [1] over a period of 356 years. So that's a total of 8 people per year. And of course that was throughout the entire Spanish Empire and not just modern day Spain. So, in other words, on average substantially more people were killed by lightning per year than by the Spanish Inquisition.
The reason not to get on a high horse over it however is simply because comparing the norms of one time to the norms of another is quite pointless. The Romans did great things and they did awful things. Like pretty much every culture to have ever existed and most likely like every culture that ever will exist. And comparing which did worse, outside of obvious extremes, is not meaningful if even possible.
I'm just saying we shouldn't get on a high horse about "death spectacles".