Agile Software Development is an "umbrella term" - a name for a whole family of approaches to software development which share a common set of values and principles. It was coined by a number of proponents of different (at that time known as "lightweight") processes, who met to discuss their similarities and found enough of them to together write and sign the "Agile Manifesto". See http://agilemanifesto.org/history.html for a nice to read story about how "Agile" came into being.
Lean Software Development applies the values and principles of Lean Manufacturing to the development of software. As far as I can tell, Mary and Tom didn't sign the Agile Manifesto, but Lean Software Development is more or less accepted by the Agile community to be compatible with the Agile values and principles - that is, to be part of the family of Agile Software Development approaches.
The soul is dyed the color of its thoughts. Think only on those things that are in line with your principles and can bear the light of day. The content of your character is your choice. Day by day, what you do is who you become. Your integrity is your destiny - it is the light that guides your way. - Heraclitus