What terminology should we use and when - 'proper' mathematical terms or everyday language?

Preparatory questions and links:

Focusing questions:
Does the introduction of terminology come before or after the concept?
At what level and/or age should you start making the distinctions between closely related concepts, eg integers and natural numbers?
Do you give students definitions or get them to make their own? What processes do you use to test definitions?
Is it worth investing in a maths and/or science dictionary, or can you rely on online information? What problems or confusions can arise when using newly introduced terminology?
How consistent are you in your own use of terminology?
Do you/should you teach the Greek alphabet and how to write it?
How do mathematical topics differ from subject areas?

(Provided by @ColinTGraham )

Useful links:
By Jenny Eather - A Maths Dictionary for Kids
By Luis Anthony Ast - Greek Alphabet (US pronunciation)
By MathProPress - List of Mathematics Dictionaries
By Wikipedia -List of Mathematics Topics
By Gary Davis - The strangeness of mathematical language (blog post)
By N S Gill - Etymology of Geometry Terms

Threaded discussion from Thursday 30th September 2010 -
Threaded discussion from Monday 4th October 2010 -

Links mentioned in the discussions, with contributor:

Resources (costing money!) mentioned in the discussions, with contributor:

Other links which may be useful