different between か and が
I am trying to learn the months in Japanese. The word for month is gatsu 月 (かつ), but when I check, か is pronounced ka, not ga and I'm a little confused. Am I understanding something wrong?

Question

Answer

I think that your source must have transcribed the reading wrong. The readings for 月 are:
つき (tsuki) when standalone speaking about the moon
がつ (gatsu) when in reference to the months (January, etc.)
げつ (getsu) when counting months as a time frame 二ヶ月 (nika/getsu, two months).

I hope that helps!

Answer

Every month 1 to 12 you have to say "gatsu". 
    ichi-gatsu
    ni-gatsu
    san-gatsu
      :
      :
      :

There is actually no "katsu" reading for 月.
There are "getsu" or "gatsu" besides "tsuki"  for example

夕月　（yuu getsu）
　年月　（nen getsu）  -> time
　正月　（shou gatsu） -> new year
　一ヶ月　(ikka getsu)  -> one month = for all numbers

But if you learn "Japanese" month of the year, it will be more difficult, junior high school students would learn it at school.
  Mutsuki = Jan
  Kisaragi = Feb
  Yayoi = Mar
  Uzuki = Apr
  Satsuki = May
    : 
    :
I wish that you did not mention it.

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