It would probably be helpful to back up a bit and talk about "buttermilk". Traditional buttermilk is the milk left over after you make butter. There are 2 kinds of butter: cultured butter (also known as Normandy Butter or Irish Butter because that's where it was often made intentionally like that) and normal butter. Butter is made by allowing the cream to rise in the milk. You skim the cream off the top and then you make butter from the cream. Before you had refrigeration, the milk would sit at room temperature and slowly sour due to the natural bacteria in it. With cultured butter, you let the milk sour a lot before you made the butter. With normal butter you wouldn't. These days the cream is separated using a centrifuge or other separator and so the milk does not sour at all before the butter is made. In the old days, though, the milk would have to sour at least a little bit before the cream would rise enough to make butter.
In the old days, the skimmed milk that was left over was called "butter milk". Keep in mind that you let the cream rise, you may or may not let it sour a bit before skimming the cream, then you skim the cream and then the milk sits around for a while before you use it -- all without refrigeration. So it sours to the point of being a kind of yogurt. The bacteria is a room temperature yogurt (technically known as a "mesophilic" culture: "meso" means "medium" and "philic" means "loves", which means that it loves medium temperatures). Mesophilic cultures in raw milk have some bacteria that produces a chemical called "diacetyl". That's the same chemical that's used to make margarine taste like butter and your movie "hot buttered popcorn" taste like super butter. It's also what makes "cultured butter" taste like butter on steroids. (If you've never had cultured butter, search it out -- you'll never want to eat normal butter again). The long and the short of it is that the kind of yogurt that you get after you let "butter milk" sit around at room temperature tastes very buttery (it's what's left over from butter and it tastes buttery -- buttermilk). Yogurt from mesophilic cultures (butter milk) tend to be less thick than warm temperature yogurts ("normal" yogurt -- also known as "thermophilic" yogurt: "Thermo" means "warm, "philic" means "loves. "loves warm temperatures"). Butter milk is skimmed and so there is also not much fat which also makes it less thick. So you get this thin, buttery yogurt that you can drink.
Of course, there is no reason why you need to drink skimmed "butter milk". Full fat butter milk tastes even better. So that's what you buy in the store. They add a mesophilic culture to full fat milk and let it acidify until you get a kind of buttery drinking yogurt. It's even better if you use half and half cream (18% fat). This is known as "sour cream" and you've probably eaten it before :-) It's even more better (grammar fail!) if you use full cream (36% fat) and that's known as creme fraiche. They are all made using the exact same technique and are essentially the exact same thing with different fat content.
You are correct that fromage blanc is basically butter milk with drop of rennet in it. I honestly don't recommend buying the "fromage blanc" starters with rennet in them. I think they are an over priced rip off, though I understand why some producers sell them -- mainly because beginners demand it. What you want is milk (skimmed or full fat, depending on your preference) and an "aromatic mesophilic culture". "Aromatic" means that it produces that butter aroma/flavour. Flora Danica is a good and relatively inexpensive one for that, but any aromatic mesophilic culture will do. You can also buy live butter milk, sour cream or creme fraiche as a starter too. Check the ingredients, though, because some of these are just milk, lactic acid and diacetyl rather than cultured live products. Anyway, you add the recommended amount of starter culture (or about 1 tablespoon of buttermilk, etc per liter/quart of milk that you are using). Then 1 drop of single strength liquid rennet. Finally, I recommend 4 drops of calcium chloride. The last ingredient may not be absolutely necessary for this recipe, but it's a good safety net to ensure that the rennet works and I haven't actually tested to see if it works without it (theoretically it probably will). (Edit: With raw milk you do *not* need calcium chloride, for technical reasons)
The problem with gritty fromage blanc is likely due to over acidification before draining. Unfortunately you can't just leave it for a set period of time. You have to watch it. The idea is that you want to drain it when the curd *just* starts separating from the sides of the container and/or whey starts to pool on top of the curd. As soon as it gets to that point, it's time to drain it. If you wait too long, the curd will essentially seize when it hits the point where it would curdle due to acidity. You are absolutely right to say that it becomes like cottage cheese because that's one of the secrets of making cottage cheese ;-) (that's a whole other conversation though -- good cottage cheese is an incredibly deep topic). Because you are using raw milk, you also have bacteria from the milk so your milk is acidifying very quickly. You really need to keep an eye on it. I wouldn't be surprised if your fromage blanc is ready to drain in 5 hours or even less.
Sorry for the information overload! This is one of those "very easy to make", but "very easy to make badly" cheeses :-) I hope this gives you some insights on how to improve.
