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 following sections for more information:
To know how to Commission & Configure Control Devices, click here
To know regarding Space settings, click here
To configure Scenes & Animations, click here
To configure Motion Based Automation, click here
To configure Daylight Harvesting, click here
To configure Light Schedules, click here