Prepare a water bath canner, jars, and lids. Keep everything hot.
Peel, core, and slice the apples into a large, heavy-bottomed pot. Peel and pit the peaches and add them to the pot (or leave both unpeeled if you'll use a food mill).
Add the water or juice, cover, and bring to a boil. Reduce to a simmer and cook, stirring often, until the apples are very soft and the peaches have broken down, about 20 to 30 minutes.
Puree the mixture with a food mill or immersion blender to a smooth, even sauce with no large chunks.
Taste and add sugar if desired, then return the sauce to a full boil.
Ladle the hot sauce into hot jars, leaving 1/2 inch headspace. Remove air bubbles, wipe rims, and apply lids and rings to fingertip tight.
Process in a boiling water bath for 15 minutes for pints and half pints, or 20 minutes for quarts, adjusting for altitude.
Let jars rest in the canner 5 minutes, then cool undisturbed for 12 to 24 hours before checking seals.