Yes, this is gluten free
Fat is not protein, and gluten is a protein. A refined oil carries essentially nothing of the seed it was pressed from, which is why even wheat germ oil is gluten-free while wheat germ is not. The only thing worth thinking about with an oil is shared frying — a dedicated bottle on a shelf is fine, oil that has fried breaded food is not, and that is a question about a kitchen rather than a label.
shortening is covered by CiCi's entry on oils and fats, which share this answer and the reasoning behind it.
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.