What is Kindle?
Kindle is an E ink device that is good for reading novels and other text books. Battery life of kindle is measured in weeks, months or days.
What is Kindle Fire?
It is a LCD tablet like iPad. In Kindle fire you can see images, videos and other short reading sessions. It is perfect in dark also and its battery life is not measured in weeks or days. It is measured in hours.
Source:
http://www.anextweb.com/differences/difference-between-kindle-and-kindle-fire/