month, moon
月 centers on the moon and its cycle: the moon itself, and the month as a unit of time based on that cycle.
Moon
counter for months
this month
every month; each month; monthly
Monday
Monday
end of the month
last month
New Year (esp. first three days)
next month
monthly publication; monthly issue
monthly sum; monthly amount
month-long period; month
monthly income
full moon
months and years
monthly salary
birth date; date of birth; DOB
full moon; moon on the 15th day of the month (by the lunar calendar)
crescent moon; young moon
one month
month and day (of the year); (the) date
time; years; days; (one's) life
half-moon
月 is a pictograph of a crescent moon. The modern form retains the curved outer shape and the inner strokes representing the moon's features.
The curved outer strokes suggest the crescent shape of the moon, and the two inner lines mark its surface. See the moon and think of a month passing.
For ゲツ, imagine a moon that looks like a giant glowing geta sandal in the sky: geta -> ゲツ, and the moon's shape reminds you of the sandal's wooden base.