Milla and Millat are the same word, there is no difference between them in Arabic. It is the same as Fatima, Khadija or Aisha. If we say "Ibrahim's creed", in Arabic it is Millata ibrahim, and if we say "Khadija, wife of the Prophet ﷺ", we say Khadijatu zawjil rasool. And if you listen to the Quran, you never hear the name Muhammad, it is always Muhammadun or Muhammadin. When we take a word out of its context, it loses the final part of the word, thus we say Muhammad, Khadija or Milla.
Other examples of words like these are Ibada, Tawba, Kabira and Mubaraka.