The difference is there are actually formal guarantees wrt privacy - such as k anonymiy, l diversity, and differential privacy.
If you can PROVE anonymiy (to a certain extent), theres little privacy issue.
The problem is that, frankly, lots of people have no idea what they're doing (or are just lying about it) – claiming location data is anonymous (it doesn't take many data points over time to identify someone), or that datasets with names removed are anonymous (they're deidentified, and the remaining attributes might be enough to identify someone).
If you can PROVE anonymiy (to a certain extent), theres little privacy issue.
The problem is that, frankly, lots of people have no idea what they're doing (or are just lying about it) – claiming location data is anonymous (it doesn't take many data points over time to identify someone), or that datasets with names removed are anonymous (they're deidentified, and the remaining attributes might be enough to identify someone).