The foods determine how much HP and stamina you have while 'under the influence' of those foods... Foods only increase your HP and stamina 'pools'...The increased values of those stats gradually decline as the food timers tick down and the foods begin to flash when the timer is about to expire, signalling you to refresh the timer by eating another piece of food.

The actual healing RATE is not determined from which foods you eat, but from having (or not having) a rested bonus, which is provided by sitting near a fire for a short time.

The rested bonus provides a +50% HP regen increase and +100% stamina regen increase over natural healing rates.

The amount of time that rested bonus lasts can be extended for longer periods of time by having additional 'comfort' items nearby while resting. These items include things such as rugs, beds, braziers, banners etc. and can potentially give you nearly 30 minutes of rested bonus if every possible comfort item is present within range of your resting spot. The bonus is always the same healing rates and the only thing that changes is the amount of time that rested bonus lasts, depending on how many comfort items were present while resting.