IDEA
An idea in the design process is an original thought,something to try out,
explore and experiment with.
For example:if designing an identity for a Fitness centre,an idea may be to focus on the health benefits of exercise.
CONCEPT
A concept is a finished proposal,which incorporates an original idea but
also addresses the relevant objectives identified in the design problem.
To continue the example:the finished concept would have refined the original idea of promoting health benefits but it also ensures that proposal adresses any relevant research findings and meets the needs of the client.
"The reasoning behind an idea,strategy,or proposal with particular emphasis placed on the benefits brought on by that idea.Examples of concepts include the design for a new automobile or the pitch behind an advertising campaign."