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.
A Later Pair of Records
Record C shows full Moon: almost all the visible disk is bright. A later record D in the same phase cycle shows third quarter: about half the visible disk is bright. Neither record is an eclipse. The supplied pictures replace any outdoor observation; never look directly at the Sun.