What factors distinguish a paper for class from a note (or e-mail) to a friend?

Answer 1

Papers:
FORMAL.
NO CHATSPEAK.
No contractions.
No first person (I, we).
No second person (you, y'all).
No slang. Use your judgement.
No swearing.
Expand on your ideas, don't assume the reader knows all the facts, but don't go on and on either.
No references to specific people whom you know personally but aren't famous.
No insults.
No personal opinion.

Notes/e-mail:
Informal, mostly.
Chatspeak allowed.
Inside jokes.
First person.
Second person.
Contractions.
Slang/swearing. (Sometimes.)
Referencing specific people (My teacher's momma's so fat she was baptised in Seaworld!)
Insults.
Heck, I've never written an e-mail with no personal opinion!

Answer 2

formality in style and grammar and the level of intimacy

In a paper, you write as though you don't know who is going to read it. In an email, there is a certain amount of understanding of who the audience is.

Answer 3

the formality, grammer, and spelling ( slang )

Answer 4

formality