In the 14th century, parmesan (as just one example) was already being made and shipped potentially as far as England. In lowland areas of the northern Mediterranean these kinds of salty cheeses were produced and easily shipped compared to the kinds being made and consumed at higher altitudes. Aged cheeses were being produced not just in the mediterranean but further north as well. Cheese production was also somewhat commercialised at that point with Monasteries conducing cheesemaking operations on a larger scale than what you'd do at home. According to Paul Kindstedt's Cheese and Culture, the already well established cheesmakers came under grater economic pressures to improve their techniques, which allowed for an increase in production, but by then the variety between different types of cheese was already pretty significant. Things like ageing and different ingredients and different styles were already well established at that point.

Is there a reason you're asking about the 14th century specifically? You can read the first few parts of Kindstedt's book on Google Books, but not as far as the 14th century. Still, if you're interested in the earlier periods, you should be able to get a pretty good idea there. It's a pretty interesting book if you're a fan of both history and cheese, which I happen to be.

Source:

• Cheese and Culture. A History of Cheese and Its Place in Western Civilization by Paul Kindstedt

Many varieties of hard cheese such as cheddar were being made as they can be kept for a long time. According to the book What the King Ate and Wizards Drank by Krista D. Ball, buying an individual slice of hard cheese was difficult and farmers were more willing to sell an entire wheel of cheese. In addition the same variety of cheese used to be wildly different colors due to time of the year and cattle feed used. Cottage cheese is very simple to make and were also common. Outside England Mozzarella cheese existed as early as 13th century.

Wensleydale Cheese.

"The historical tradition of cheesemaking in the area dates back through centuries. The cheese was first made in the area by French Cistercian monks who settled in the 11th and 12th centuries. Evidence suggests that the monks of Wensleydale became proficient farmers and were skilled in animal husbandry, and cheese making from the milk became a valuable source of food. It is acknowledged that the early monastic cheese was made from sheep’s milk, but cow’s milk became the dominant source of milk following the dissolution of the monasteries in the 16th century." Official Journal of the European Union.

http://eur-lex.europa.eu/LexUriServ/LexUriServ.do?uri=OJ:C:2013:231:0020:0024:EN:PDF