Should I type
elementary OS or
What's the difference between
Should I call the system
elementary is the name used for the entire project (operating system and everything else related to it).
elementary OS is just the name of the operating system, not the entire project.
elementary's team prefers typing its name with a lowercase
e for consistency. So, you should always type
elementary instead of
Elementary (even if it's in the beginning of the sentence).
elementary's team prefers that you do not refer to
elementary OS as
eOS because that kind of mimics Apple's
KThis and GNOME's
GThat trends, which they're trying to avoid.
Source: The Importance of Our Brand (Internal Branding Guidelines section)
Further reading: Let's enforce branding guidelines in edits (meta post)