DNA is not exact- they cannot predict a precise relationship between two people based on common DNA, only a range of possible relationships for the results. This gets less reliable with more generations of separation and the two testers share less and less DNA. You'll find that sometimes even if you match with two full blood siblings on another side of the family they might not show up with the same predicted relationship to you because they've inherited different sections of parental DNA. DNA is quirky like that.
As far as your aunt is concerned a first cousin prediction is not that far out, especially since she shares only one parent with your side. That kind of thing pushes the prediction out slightly because you match her closely, but not as closely as if she'd been a full aunt. As such, the goalposts have been moved a degree outwards and you have suggestions for a marginally more distant relationship.