Is cooking with an air fryer similar, nutritionally, to baking?
Using an air fryer without oil is essentially the same thing as using a convection oven. This would make it no more and no less fatty than baking. If you use oil in the air fryer then my understanding is that you are being marginally less fatty than deep frying because the saturation in oil is just not as significant.

Incidentally your use of oil in a baking/grilling setting are not quite similar because the oil is allowed to drip off, it is not continuously reapplied or applied at the top and allowed to soak down. Rather it is usually on the bottom surface to prevent sticking (Note: basting with the oil would cause the food to absorb more of the fat and thus be fattier.)