In religion, the laws of nature are
1. part of the realm of divine powers and therefore not researchable by humans
2. infallible
In the Renaissance, christian scholars (frustrated with the doctrine-laden ways of the Catholic Church) tried to go back to the original version of Christianity.
This is how the Middle-Ages ended and the Renaissance began.
They stumbled upon esoteric texts from ancient Greece from 200 AD, which sought to combine christian, jewish and egyptian teachings. These books were the Corpus Hermeticum and the Asclepius. Due to a dating-error that had happened ~300 AD, they were thought to be from Ancient Egypt. So these christian scholars found a text from "Ancient Egypt" that contained hints at Christianity. That's how the magical teachings of the Hermeticists entered the mainstream.
(The medieval mystician Ramon Llull also played a crucial role, but it would go too far to elaborate on that.)
In the Renaissance-magic, the laws of nature are
1. separate from the realm of divine powers (-> Llull), and the human has the possibility to access them by magical means due to his divine heritage
2. infallible
During the Renaissance, these scholars tried to find these magical laws that would give them control over the forces of nature via experiments. They did so in secrecy, because the Catholic Church still wasn't sure whether this "magic" the hermetic texts are speaking about comes from God or from demons.
Giordano Bruno made the mistake of drawing too much attention to his works and drifting too far away from mainstream-Christianity.
The magical laws turned out to be failures. None of the experiments worked. Eventually, advancements in mathematics unearthed a further set of "laws of nature". From now on, the scholars, the magi, the researchers tried to incorporate math into their experiments. The goal switched from qualitative explanations to quantitative explanations.
The researchers knew they had developed a new method of gaining knowledge but they had no idea how to classify it. They just called it "the method".
This is how the Renaissance ended and the Age of Enlightenment began.
In science, the laws of nature are:
1. independent from a divine realm and researchable by the humans
2. fallible