What is the difference between 日 and 号?
Note: I use trad.Chi so 號 is the same as 号

When you talk about a date, you can use 號 when you are talking casually with people, for example:


  今天是幾多號？
  今天是十五號。


You can use 日 when you're writing (eg. diary or notes) or saying something formal:


  十二月八日


Both has the same meaning.

[!] If you use them for other meanings, they are totally different.