It depends on where you are
Derived from the oat hull. Naturally gluten-free but subject to the same field and mill contamination as any other oat ingredient, so it needs certification rather than assumption.
The insoluble hull of the oat, milled fine. Almost pure cellulose, almost no starch and almost no protein — which is why it has become a staple of low-carb and keto baking, where it adds structure and fibre without carbohydrate.
Because it arrives from a direction most people are not watching. Somebody managing coeliac disease learns the rules about oats and then meets oat fibre in a keto bread or a protein bar, in a context framed entirely around carbohydrate rather than gluten, with no mention of certification anywhere on the packet.
Check for certification exactly as you would with rolled oats, and do not let the low-carb framing of the product change how you read it. The avenin question applies too: if you are among the minority who react to the oat protein itself, trace protein in the hull is still oat protein.
The answer changes by country. CiCi applies the rules for wherever you are, and will tell you when a product that is fine at home would not qualify where you are travelling.
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.
The aisle guides below cover Oat fiber in context — which is usually the more useful question, because an ingredient rarely appears alone.
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.