I'm afraid I must begin my answer with a disclaimer: I am not a Inquisition historian and my area is somewhere else. That said, let me see what we can do.

The Spanish Inquisition, and inquisitions im general, were definetively 'a thing' (whatever that may be). There has been a quite annoying group of catholic 'historians' trying to deny it because, well, it makes them look bad. So watch out for that, Inquisition denial is harder to spot than other more famous movements...

With that out of the way, the historians I know generally argue that the Spanish Inquisition started in 1478, when Pope Sixtus IV issued a bull giving supreme authority to Ferdinand and Isabel (and their respective heirs) to name Inquisitors and virtually control the Holy Office in their country and later, in the viceroyalties. If not at that date, generally one or two decades after that.

During its existence, which lasted all the way into the 19th century (though with far less power in the last centuries), the Spanish Inquisition held several tribunals, with three in the Americas (Mexico, Lima and Cartagena de las Indias), and at least eleven in mainland Spain. Meanwhile, for comparison, the Portuguese Inquisition only held four tribunals, three in the mainland and one in Goa.

Just as I said that there is a recent movement of Inquisition denial, back in the 17th onwards, there has been a movement led by Enlightment authors against the Inquisition, and they became quite famous for exaggerating the "overzealousness" of the Inquisitors, their hipocrisy and corruption. Since some of those authors weren't exactly fans of the monarchy and the catholic church, you can see why that is.

But that's besides the point. What I believe it really needs to be answered is TL;DR: The Spanish Inquisition was definitively 'a thing', it was a literal fusion of Church and State, it started in the late 15th century, it held several autos-da-fé, with trial documents available from at least five different countries.

And to finish this, a recommended read is Bethencourt's book "The Inquisition, a Global History", recently (2009) published in a new edition by Cambridge University Press.

r/BadukNak has already written an excellent answer. I'll add a few bits from my perspective. I am also not an Inquisition historian, but there are Inquisition historians (such as the Bethencourt book cited in r/BadukNak's answer) and I did study it previously.

As there are Inquisition historians, part 1 of responding to Preston's point is that if you ask those Inquisition historians they will tell you in great detail why and how it was a thing (alongside the Italian Inquisition and others in other Catholic countries and their colonies).

Part 2 of Preston's point implies that what we think of as the Inquisition existed before and afterwards and that it can't be tied to any broader change or trend in political or religious culture. This is patently false - the Inquisition(s) were one of the key parts of Catholicism's response to what was arguably the biggest crisis in its history, the Counter-Reformation. There were certainly other major crises (the Great Schism with Constantinople comes to mind, or heresies which held different interpretations of scripture), but I can't think of anything which caused such a fundamental crisis of identity in the established Catholic Church.

Before the Protestant Reformation in the 16th century, the Catholic Church had grown to become a hugely powerful entity. Following its initial post-Roman expansion and conversion of Europe, the Bishop of Rome had successfully pivoted into wielding political power (through becoming the religious authority behind European monarchies) and military power through the use of religious power to authorise the Crusades in the 11th-13th centuries. The Church held immense influence, power, and most importantly for us, wealth, and it abused all of these things (e.g. selling off plenary indulgences, which is comparable to the scandal around the sale of titles in the UK). The reason Luther's 95 Theses document was written, why it was posted so publicly and why it took off so strongly was because Christianity was supposed to be a religion of the poor in service to God, but those holding Church offices were living lavish lifestyles. It was essentially a catastrophic wealth scandal.

Protestantism therefore constituted a critical challenge to the heart of Early-Modern Catholicism, saying Catholicism was no longer reflective of true Christianity and Protestantism aimed to bring back the plainness and poverty which it saw as being a true veneration of Christianity. Protestantism said Catholicism wasn't what it claimed to be anymore.

The Catholic Church, as the incredibly rich and powerful organisation it now was, recognised the threat this posed to that power and wealth by questioning everything the Church stood for. With the Church having formed a European socio-political culture which was intensely and devoutly monotheistic (which hadn't existed before the post-Roman conversation it carried out) religious legitimacy was key. Without that, the Church had no claim to power.

The Counter-Reformation, therefore, became the race to claim being the "truly original" Christianity. Protestantism's claim was that it was going back to the Church's original culture (before the wealth and power took it off course). Catholicism's claim rested on the Papacy's long history as the centre of Western Christianity and the guardian of orthodoxy. This meant that, where before the Church had grown lax in its duties and the rich clergy had become concerned only with their own wealth and power, now the Church had to double down on its commitment to religious orthodoxy.

Part of this was holding the Council of Trent to confirm what it actually agreed at this point and set out or refresh various Church laws. The other part was to go out and actually reconnect with its people to ensure their beliefs were orthodox (and punish them if they were not). At this point, the impression of sources is that the Church genuinely believed that most people understood Catholic orthodoxy because (going back to the social bubble that was Catholic clergy culture) most of the clergy, especially at a higher level, never encountered anyone who did not hold the same core assumptions as them about Christianity.

The Church, however, was in for a shock. It had done such a poor job of communicating Catholic orthodoxy that beliefs varied widely and in ways which were completely unthinkable for the clergy. The most extreme examples were remote communities which, when contacted, barely spoke the same language as the visiting clergy because they had not been in contact with the wider community for decades or even hundreds of years. Another classic example (though from the Italian reformation) is the miller in The Cheese and the Worms (a microhistory by Carlo Ginzburg) who unwittingly told his inquisitors severe heresies (e.g. Mary couldn't have been a virgin because she had a child, Jesus).

The Inquisition, then, was the Catholic Church's heavy-handed response to this utter shock. Not only had Protestantism fundamentally questioned Catholicism's legitimacy and its right to lead the Western Christian world, but it had turned out to be correct! Catholicism had been doing a bad job of properly teaching its people.

As with all large and powerful organisations when threatened, the Church took action to enforce its (sometimes newly refreshed at Trent) rules by setting up Inquisitions in all major Catholic countries and their colonies. These functioned as essentially religious courts which would accuse someone of holding improper beliefs, interview the accused and any witnesses, hold trials where a sentence would be decided, then enforce that sentence.

These were bizarre in practice for several reasons:

1. The gulf in religious norms between inquisitors and the accused was sometimes so great (as in The Cheese and the Worms) that neither understood each other. This obviously made questioning and giving correct answers very difficult. It was easy to trip up (as did the miller in the above book, who was executed for his unwitting errors).

2. There were already normal courts as part of the existing legal process! Inquisitorial courts would end up arguing with the existing legal courts about who got to prosecute defendants.

3. As with any attack on a wealthy and powerful organisation, the defense was less about whether individuals did anything wrong and more about making a show of political force at the right times. This meant that when a spectacle was needed, an auto da fe would be planned. This was essentially a parade of everyone who was accused and their sentences would be carried out at the same time. When an auto da fe was announced, Inquisitorial courts would find as many people to accuse as they could, mostly of minor religious crimes which would have equally minimal sentences like wearing a hair shirt. There would always be major crimes, though, and the auto da fe would end with a mass sentencing and execution in the main city square. E.g. Logroño was the main Inquisition city for the Basque region of Spain.

So the actual acts of the Inquisitions could be sporadic, but absolutely happened. Many people were accused and executed as a result of this religious crackdown.

The Catholic Church actually came out of this Counter-Reformation period stronger and its popes were sometimes even more extravagant in the 17th century.

Books recommended include:

• The Cheese and the Worms by Carlo Ginzburg.
• The Papal Prince by Paolo Prodi.
• The Inquisition: a Global History by Francisco Bethencourt.
• The Italian Inquisition by Christopher F. Black.

While you wait for an answer to your specific question, there are several earlier answers which may provide context, while presenting somewhat different conclusions and views of the historiography.

This thread with contributions by u/sunagainstgold and u/kieslowskifan

And this answer

And this answer by by u/TywinDeVillena