Outside an eclipse, sunlight reaches roughly half the whole Moon. As the Moon orbits Earth, our view of that sunlit half changes. The Moon stays whole. Quarter is a phase name: about half the visible disk looks bright at first or third quarter. Ordinary phases are not Earth-shadow events.
Worked example
A first-quarter picture has about half its visible disk bright. A full-Moon picture has almost the entire visible disk bright. Roughly half the whole Moon is sunlit in both cases. These are two selected stages, not every phase.
Two Selected Picture Records
Record A shows first quarter: about half the visible disk is bright. A later record B in the same phase cycle shows full Moon: almost all the visible disk is bright. Neither record is an eclipse. Use these supplied records, not an outdoor observation; never look directly at the Sun.