By PC I assume you mean a Wndows PC. The PC's OS is the important thing.
Configurations are mutually exclusive, the device can only be in one at once. It is vey rare to find a device with multiple configurations, I only know of one company which has bothered to make it work (the one I used to work for). The big problem with configurations is Windows only supports one configuration by default. To enable multiple configurations for your device you need to write a custom device driver, which most people don't have the ability to do (including you and me it seems.)
Interfaces are not mutually exclusive, they work at the same time as each other. A device where its functionality is determined by its interfaces is called a composite device. Most devices in the world are composite devices, though they usually only have one interface, and thus one function. However multiple (concurrent) interfaces are supported on all major OSs. So there are a large selection of devices in the world which have multiple interfaces. Each interface enumerates as its own function, largely independent of the other interfaces in the device.
You have two interfaces, VCP and Log. With configurations it would look like this:
Configuration 1:
VCP
Configuration 2:
Log
You can have one or the other, you have to arrange to send a set configuration to switch between the two device modes.
With interfaces it'd look like this:
Configuration 1:
VCP (interface 1)
Log (interface 2)
The OS will enumerate the VCP port as a standard device, it'll let whatever driver you use for the log to attach to the other. Both can work at the same time. My current device can look exactly like that, and both the VCP and log interfaces work independently at the same time.