Lesser demigods are powerful entities to be sure, but are generally obscure and don't have too many followers, if any. Many of these demigods are the children of other demigods or actual gods, and have attained power and immortality through their blood. Others are mortals have have ascended to demigodhood through respect for their power alone.
Generally, those considered demigods are still constrained to a physical form most of the time, and are often very mortal, even though most have great longevity. Commonly they will be associated with a mortal race, and will ordinarily take a suitable form reminiscent of it.
Demigods often choose champions in order to spread their influence and power. They will grant minor boons to these champions to keep them alive.