It depends
The word doing the work is "food", not "modified" — modified only means the starch has been treated to change how it thickens, which tells you nothing about what it came from. On an FDA-regulated packaged food it is corn unless the label says wheat, because wheat is a major food allergen and must be declared. On a USDA-regulated product — meat, poultry or egg — only the common name is required, so this can be wheat starch and the label need never say so. Same three words, two different guarantees, and which one applies depends on what kind of food you are holding.
Because the answer depends on the rest of the label, scanning the actual product is the only way to resolve it — CiCi checks for a gluten-free claim, the allergen statement, and which agency regulates that label, then tells you which way it lands.
food starch modified is one of the names CiCi tracks for Modified food starch. Ingredient lists use many names for the same thing, which is a large part of why gluten slips past careful readers.
Every one of these is the same ingredient. The number of names is a large part of why gluten slips past people who read every label.
Point CiCi at the barcode on the product you're holding and get this same reasoning in about two seconds, plus the carbs and the full nutrition panel. 360,000+ packaged foods are already read and waiting.
This answer comes from CiCi's ingredient lexicon — the same rules the scanner uses, not a separate article. Where reputable sources disagree, CiCi takes the conservative position and says so.