More properly it the term is coagulating agent. All cheese starts with a curd, there are several ways to create curds in the milk of choice with differing taste and texture impacts. What comes next has a large impact on the result. How large do you cut the curds? How much are they stirred? Are they cooked? How hard are they pressed? How is the resulting cheese aged.
The Farmers Cheese recipe probably formed a loose ricotta like curd which was drained in cheesecloth, right? You can also use lemon juice for a slightly different flavor The mozzarella had to have something to acidify the milk before adding the rennet. Was there a culture or citric acid added? After setting the curds are cooked and pulled - the cooking and stretching transforms the cheese. Many simple cheeses seem to me to be local variations on a theme - Farmers' cheese is approximately the same as Paneer.
When I was a real newbie (not the lightly experienced newb I am now) Many cheese recipes seemed so similar I couldn't see much difference. The more I have learned, it is amazing how subtle differences in preparation can create different cheeses. For example, Monatsio and Manchengo recipes are very similar. slightly different culture mix, slightly different temperatures and you get similar but distinct cheeses.
I think it was on the Washington Cheese Guild's Stilton approximation page that I learned that a 2 degree F change in ripening temperature can affect the final product's taste. Most commercial cultures are a mix of different types of bacteria, and a subtle change in temperature can favor one type over another with a change in the resulting cheese.
There is a lot of information on this board and the wiki, read as much as you can. Then get into the kitchen, sterilize everything (learned the hard way how important that is) and make some cheese. Keep good records of your make (there is a form somewhere on the board that will help you track your make - it also gives some idea of the number of variables there are in cheese making). There are a lot of helpful people here, post questions and you'll get a number of responses. Post a thread about your make and people will answer questions you didn't know enough to ask. One of the best things about this board is that the people with the most knowledge are usually the first to reply. The usual progression is from a fresh cheese like a Farmer's to an aged cheese - Caerphilly is a short aging cheese that will give you quick feedback. Long aging and mold ripened cheeses are a bit trickier, probably best to put them off until you are getting consistently good results with short aging cheeses.
Happy cheese making! And eating.