What are the examples of 'formal' and 'informal' communication?

Words containing an apostrophe to replace a letter could be classed as informal English, for example: I've instead of I have, shouldn't instead of should not, etc.

In correspondence, Hi Jim ... Best wishes could be classed as informal English, whereas Dear Sir ... Yours faithfully would be formal.

Formal Dear Sir: Please mail a copy of your book to the following address.

Informal Yo, dude, slip these guys one of your things, ok?