Farmhouse cheddar: history of being made in small batches. Can be milled or stirred curd. This name is sort of pointless because there's nothing truly distinctive about it, it's a cheddar like other cheddars. It's like saying there's a huge difference between artisan and commercial cheddar in terms of their technologies (there isn't, artisan is about smaller batches).
Stirred curd cheddar: made to save the labor of milling curd. When done right, the results can be very good.
Milled curd cheddar: This is where you stack slabs, flip them, and let the acidity build up.
Cheddaring builds up acidity and also orients the direction of the strands of joined micelles in the cheese. Or to look at it another way, when the acid builds up, the micelles can slide over each other, and the stacking process stretches them out ever so slightly. There's been some research to suggest that the orientation is not crucial for flavor formation, but that the combination of fusing at lower pH and salting the individual curds is what gives the flavor.