In addition to sunshine and moonshine, there is earthshine.
If you are looking for a partial moon during the day (even without binoculars), if the moon is in the sky, far enough away from the sun that you aren’t blinded, and is in the right phase, you can supposedly see the part of the moon that is illuminated by the sun, but instead of the rest of the moon being black because of the shadow the earth casts, you see earthshine, because the sunlight reflecting off the earth illuminates the shadow a little.
I heard recently that a poet called it “the old moon in the new moons arms,” or something like that.