There actually is a precise definition of "ultra-processed" foods per the NOVA Food Classification system:
Ultra-processed foods are industrial formulations made entirely or mostly from substances
extracted from foods (oils, fats, sugar, starch, and proteins), derived from food constituents
(hydrogenated fats and modified starch), or synthesized in laboratories from food substrates
or other organic sources (flavor enhancers, colors, and several food additives used to make
the product hyper-palatable). Manufacturing techniques include extrusion, moulding and
preprocessing by frying. Beverages may be ultra-processed. Group 1 foods are a small
proportion of, or are even absent from, ultra-processed products.
Processed foods are products manufactured by industry with the use of salt, sugar, oil or
other substances (Group 2) added to natural or minimally processed foods (Group 1) to
preserve or to make them more palatable. They are derived directly from foods and are
recognized as versions of the original foods. They are usually consumed as a part of or as a
side dish in culinary preparations made using natural or minimally processed foods. Most
processed foods have two or three ingredients.
There's also Unprocessed or Natural foods, Minimally processed foods and Processed Culinary Ingredients.
I'm not sure who uses these definitions and why but some seem a little shaky to me. Soybean oil would be considered a "processed culinary ingredient" along with white sugar and maple syrup from trees.
I can't argue with their examples of "ultra-processed foods" though: