very simple: "Nepali" is a day to day life ma Nepali le use garne Nepali word. the "Nepalese" is the word used by foreigner. 

We Nepali call it "Nepali" or use it "Nepali" like: "we are Nepali"; "we eat Nepali food," "we speak Nepali language," etc.

Those English and other language speaking people call or use it "Nepalese" like "they are Nepalese"; "they eat Nepalese food," "they speak Nepalese language," etc.

I have also noticed that some Nepali media use "Nepalis" for Nepali haru or for that belongs to Nepal or Nepali people.