You’re right that they’re they same. According to the Polkit Wikipedia article,

Since version 0.105, released in 2015 the name of the project was changed from PolicyKit to polkit.

Also, the tag wiki excerpt for policykit is a copy of the first line of the above Wikipedia article,

Polkit (formerly PolicyKit) is a component for controlling system-wide privileges in Unix-like operating systems.

I don’t have enough (any) reputation in these tags to suggest a synonym but I’d recommend that a moderator or high rep user change policykit to be a synonym for the newer name, polkit.

ConsoleKit (documentation) was a service which tracks user sessions (i.e. where a user is logged in). It allows switching users without logging out (many users can be logged in on the same hardware at the same time with one user active). It is also used to check if a session is "local" i.e. if a user has direct access to hardware (which may be considered more secure than remote access).

Currently the ConsoleKit is largely replaced by logind, which is part of systemd, although there is standalone version elogind.

polkit (née PolicyKit) documentation allows fine-tuned capabilities in a desktop environment. Traditionally only a privileged user (root) was allowed to configure network. However, while in a server environment it is a reasonable assumption that it would be too limiting to not be allowed to connect to a hotspot on laptop, for example. However, you may still not want to give full privileges to this person (like installing programs) or may want to limit options for some people (for example on your children laptops only 'trusted' networks with parental filters can be used). As far as I remember it works like:

• Program send message to daemon via dbus about action
• Daemon uses polkit libraries/configuration (in fact polkit daemon) to determine if a user is allowed to perform an action. It may happen that certain conditions must be fulfilled (like entering password or hardware access).
• Daemon performs action according to it (returns auth error or performs action)