I'd say we've a more formal working relationship - formal in an HE, not a armed forces way - and the email is in response to an earlier email articulating some problems with our Elgg (an open source SNS) installation.
Sections of the earlier email are quoted and answers fairly brief. Key issues are explained and a way forward outlined. There's no conversational joking - it's all to-the-point, professional stuff.
I tend to use email in lieu of a phone call, especially when:
- multiple recipients are involved
- I want to leave an audit trail ("at today's meeting we agreed to ...")
- I'm pressed for time and want to avoid the small talk that a phone call entails ("Hi X, how are things etc., etc. ... the reason I'm calling is ...")