'Confidentiality' refers to the researcher or data collector being aware of the identity of their research participants, but ensuring that those personal identifiers are not shared; 'Anonymity' refers to situations in which even the researcher does not know the research participants' identity, such as through the use of an anonymous survey. An alternate way of looking at it is that in confidential data, personal identifiers are gathered but not shared, whereas, in anonymous data, personal identifiers are never gathered.
Note that 'anonymisation' is often used as a broad term for all sorts of de-identification activities, and does not necessarily make a distinction between confidentiality and anonymity.
