Yes, this is gluten free
Milk contains casein and whey. Neither is gluten — they are milk proteins, and the only resemblance is that both words mean protein. Plain dairy has never been a gluten question. What makes dairy worth checking is what gets added to it: a yogurt with cookie pieces, a shredded cheese dusted with starch to stop it clumping, or blue cheese, whose mould was historically grown on bread and which CiCi tracks separately.
yogurt is covered by CiCi's entry on dairy, 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.