Hi Pensee .
The configuration management plan is part of the project management plan and describes the configurable items of the project and identifies the items that will be recorded and updated so that the product of the project remains consistent and operable. (PMBOK 6th Edition Pg,88, 116)
Whereas the definition of the change management plan describes how the change requests throughout the project will be formally authorized and incorporated. (PMBOK 6th Edition Pg 88)
A change log is described as a document in which the disposition of all change requests are recorded. (PMBOK 6th Edition Pg 120)
The difference between the 3 is that the configuration management plan highlights sections or items in the project that have specific procedures for initiating and executing changes. For example in a building construction project, certain project artefacts such as drawings will be under configuration control meaning that there is a certain way that they need to be updated by involving the architect, engineer and local authority. However, the colour of the paint in the building might not be under configuration control. Change management plan then describes how any change requests are executed for all items whether they are under configuration control or not. (In our example, this applies to both the drawings and the colour of the rooms) Finally, the change log is a project artefact that describes how each change request was dispensed. This will apply to both the change requests that were accepted, deferred or rejected.
To answer your other 3 questions;
1) "...Is the change log the old school version of the configuration or change management system?..."
# No. Please refer to my explanation above.
2) "...So I understand that once a change is requested and if it impacts other project constraints, then a change request is submitted to the CCB, so do you update the change log or do you update the configuration mgmt system or the change management system?..."
# In this case you update the change log only with the dispensation of the change. For all change requests, the dispensation can either be accepted, deferred or rejected.
I hope this helps.
Best.
Eric.