Magick performed on the waxing crescent moon is very similar to the waxing gibbous moon (they are both in the waxing or increase phase) and indeed you don’t have to pay attention to the distinction between them if you choose not to, but you should be aware that the closer the moon comes to being full, the more powerful it’s increasing potency becomes. This can be useful to know because sometimes we all have the luxury to wait a few days until after the half gibbous moon has passed into the more powerful phase, the waxing gibbous phase. With rituals that require less lunar potency or are the first in a line of several consecutive rituals that lead up to the full moon, you can confidently use this phase of the moon. For example, a healing performed to ease a cold or mild chronic illness can easily be started during the waxing crescent phase of the moon. However, a more serious illness would be better served during the waxing gibbous phase.
Ideally, with some minor examples, nearly all magick would be best divided out between the full or new moon, but this is such a short period of time each month, that we delegate certain phases to certain less important tasks. However, remember two things. For very serious illnesses the full (for healing the illness) or black (for banishing the illness) moons are the best choices, but they are not always necessary for more minor problems. Also the time does come sometimes when we have no choice but to do ritual work during incompatible times. In emergency cases, don’t let bad timing stop you. Use other Nature Correspondences or the other types of magick (Mental or Spiritual Magick) to offset your lack of timing.