What does the "side-band" and "in-band" mean in the context of digital circuit?
Many digital interfaces have more than one method of passing information.  The main one is usually at high speed and takes the majority of the capability of the medium. Any information along this path is called "in-band".

However it is often necessary to communicate control or status information without disturbing the main data path - for example on HDMI there is the main video and sound transfer path but also a low speed I2C connection used to turn a TV or DvD player on or provide information on status- these are described as out-of band, or sometimes "side-band". This is completely different from the description you found that applies to modulation.

This out-of-band path may also be bi-directional even though the main data flow is unidirectional.