I'm going to provide my definitions without referencing any material. This is in a personal computing context:
Privacy: What I do on my local computer only I know, the files I read from my local hard disk, the computational operations that I perform, the text files I create, the commands that I input are known only to me (the user). These operations, inputs by keyboard and outputs to my screen / monitor are known only to the user, only I know what files I observed, how I interacted with them, edited them or saved them, and what commands I inputted to the keyboard to perform these actions. Local files and operations on the personal computer are known only to the current user, and are ephemeral and gone once the computer is power cycled, unless I specifically made a log of the actions and stored it to disk intentionally.
Security: Unauthorized users, programs, or processes are not able to access read, write or modify, or know the contents of files or operations performed on the personal computer. Remote computer users can not access, retrieve, files or memory from my personal computer unless I have set up a server to do so and only within the context of the files being served. Other persons with physical access to my computing device can not operate, or retrieve files or information from the device without authorization.
Anonymity: Actions performed in public whether observed or unobserved, are either unnoticed, noticed but unreported, or noticed and reported but it is not possible to attribute the public actions to the source actor either due to lack of observable evidence, or the computational complexity. Public here means remote computers that my personal computer connects to via internet routing technologies. Public access from my computer to another computer system hosting files or serving files and content via the internet. Actions could include retrieving files, modifying files, or reading and posting text to a remote server by way of programs running on my personal computer.
People accusing each other of not grasping the separation or overlap of these concepts is perennial (comes up often). So I figured this should be sorted out in it's own thread. Post any additional definitions or links to proper definitions below.