I have seen four different styles on how to format a date:
- 1 January 2018
- 1 January, 2018
- 1st January 2018
- 1st January, 2018
Which is used when and where? Which are common and why are there these four different types?
The formats "1 January 2018" and "1st January 2018" are both widespread in Britain.
Including a comma before the year is less common and most style guides recommend against it. It has the undesirable effect that if you start a sentence with "On 1st January, 2018", you'll probably end up also putting a comma after "2018", and whether you do or not, it just looks odd. If you use commas both before and after "2018", it then looks as though the year is a parenthetical aside (set off by commas), and yet if you omit the second comma it looks as though the year belongs to the portion of the sentence after the comma rather than the portion before it.
Using superscript for the ordinal suffix is optional.
British speakers always pronounce the "1" as "the first" even when the date is written without the ordinal suffix. The word "of" is almost always pronounced, too, even though not written.
In American English, "January 1, 2018" is a common style, and including the comma is pretty much mandatory because otherwise you have two numbers coming together in an unpleasant or confusing way.
Questions of style, rather than grammar, can only be answered by choosing to follow an established style guide or choosing the style you want to use and then being consistent. So, the only real answer here is to choose a style and follow it, consistently. The Chicago Manual of Style, for example, has an entire section on date formatting, although I don't think ordinals are ever used.
All the formats are correct, especially in BrE. In AmE, you usually write as follows:
January 1, 2018
January 1st, 2018
As for the difference between 1 January (,) 2018 and 1st January (,) 2018, the use of ordinal numbers i.e. 1st, 2nd, etc. is less common.
January 1, 2018
are far more common. And the ordinals (1st, 2nd, 3rd) are rarely used in written dates. It might have been easier to take this question seriously if you asked about more common styles and showed where you had found them; perhaps you would have had a less hostile reception at English Language Learners.