I slightly disagree with your distinction. Privacy is about minimising the amount of data collected that's visible to anyone but you. Your data stays with you and/or only you can see your data, therefore, private. Anonymity isn't about the amount of data collected, but that the data collected or accessible by others can't be linked to you.
I could have been more clear there. I was specifically thinking about data that can identify you, not just data in general.
If I'm the only one in possession with data I don't really consider it data collection at all, at least in the context of privacy and anonymity. Other than that I agree with your clarifications here though.
