Do the light controls supported by different Groups vary from each other?

Yes. A group provides light controls based on the type of light devices added to it.

For example, an RGB panel for light control will be shown only if the group has one or more RGB lights added to it

You can also visit the next sections:
To know how to create a Scene Schedule using Date option, click here
To know how to automate lighting with Motion sensors, click here
To know how to implement Daylight harvesting, click here