As I understand it, in the medieval and the earlier parts of the early modern period religious difference was rather more important than racial difference. But I will let someone else who knows more speak about that. My answer will cover the period from 1720-1820 ish.

Personally I would place the development of theories of race slightly later -- it was around 1820 that we really begin to see a hardening of racial attitudes. We see the publication of the first racial taxonomies based on inherent biological difference by people like Cuvier (1815) and a need in imperial circles to differentiate colonial rulers from colonial ruled. However, that is not hugely relevant to the question. Before then however both skin colour and race were seen as highly mutable and dependent of climate. So John Hunter in his inaugural dissertation includes a detailed taxonomy of people of various different skin colours -- "sub-blacks" include the "moors of north africa and the Hottentots" red skinned as the native Americans, "light brown" the Spanish, laplanders etc. However, his explanation for biological difference is explained in terms of adaptation of the climate rather than an inborn racial capacity. For him "The seat of colour is without controversy in the skin, though it is not diffused throughout that organ, but only occupies that part which is called the cuticle...Air, dirt and the heat of the sun, the transparency of the cuticle being destroyed, give it a brown colour, and at the same time make it harder." And therefore "We need not be surprised that greater blackness is thereby effected in much hotter regions where men are exposed naked to a burning sun at almost all times". As a result he also makes the argument that all black people are born white and then darken as they age -- clearly he had never come into contact with one. This was also a two way street, white people who went to hot countries would inevitably darken and become more like the natives with time. He also spends a lot of the work proving that blacks and whites are of the same species. He points to anatomy, observing that there is little to no biological difference in humans if you look under the skin, and that blacks and whites can produce healthy offspring and therefore must be of the same species.

Other contemporary authors take this logic of human mutability and biological adaptation even further. John Hunter for instance give an example of a man he knew who lived with the Native Americans for a period of time. He claimed that the man had become so acclimatised to the American climate that he could not tell him apart from the actual natives "except by his speech".

As for characteristics based on race, there were a lot of those and again they cut both ways. For whites, it was generally thought that they were generally unsuited to survive for long in tropical climates. So James Lind, the discoverer of the citrus cure for Scurvy commented in his Essay on Diseases incidental to Europeans in Hot Climates (1768) argues that "Men who thus exchange their native for a distant climate, may be considered as affected in a manner somewhat analogous to plants removed into a foreign soil" and are liable to sicken and die. As such doctors urged Europeans in places like India to adopt a whole range of, sometimes, sensible strategies to ensure that they did not fall ill. Other commentators noted that the same was true with the few blacks who came to Europe. One remarked that "The African children brought over by the sierra leone company for education seldom survived the third year in this country." The flipside was that the people of other countries had characteristics ascribed to them from the environment, which then became truly racial later on. Some argued that the apparent listlessness of the Indians was due to the heat, and indeed urged Europeans in India to imitate their manner and ways of eating (essentially to adopt vegetarianism with less ghee) to prevent themselves from getting heatstroke.