You'll want to edit the settings of the stock piles. For the one near your kitchen, you still want meat and fish enabled (among other raw ingredients you want to use to cook) and disable prepared meals by pressing u. Then for the one near your dining room, you want to first enable food (e) then block everything (b) and then you can re-enable prepared food (u) which will then only stockpile the biscuts, stew and roasts.
In a real life comparison: Prepared meals are considered things fully cooked, like what you would normally eat for breakfast, lunch or dinner. Meat and Fish are just chunks of raw meat and raw fish. Unprepared fish are freshly caught fish with things like scales, guts that need to be descaled, have their stomach and other organs removed, and perhaps even have the bones removed. Unprepared meat is just a whole cow, or dead chicken with feathers still on it. Meat (prepared for cooking) is things you'd find in a package ready to cook like a steak, or chicken breast (or thighs. I prefer dark meat/ thighs and drumsticks personally) and while it's possible to eat these things raw, they often tend to be better cooked.
For food thoughts, it doesn't matter if it's cooked or raw (unless it cannot be eaten raw like quarry bush leaves). If you don't have the desired ingredient cooked in a meal but have it sitting in your stockpile waiting to be cooked, then the dwarf will go after the raw food, desperate to eat a food they like. Like desiring a filet mignon but only being able to eat ground beef (hamburgers and meatloaf). Well, they get their hands on a filet mignon and even thought the cook hasn't been able to cook it yet, the dwarf will take it and eat it raw (maybe beef carpaccio) and still receive a content thought. But if you have a masterfully prepared bacon wrapped filet mignon on a bed of fresh greens, the dwarf will go after this instead and be deligted instead of merely content. Also, your dwarves who would rather have a plain steak won't want the filet, no matter how good it is. So food gets a bit odd that way.
Make sure you use pots for both piles, otherwise food can rot / cause miasma and your cook will be unhappy (negative thoughts) for their well made food going to waste.
Except if you're playing vanilla and have to use various methods to get liquid ingredients to be added to the food (milk, alcohol and oils). I've heard DFhack has some things that allow you to set up specific ingredents if you want to play chef (and that reminds me that I want to do that).