Kaizen is the core principal philosophy of continuous improvement, whereas Lean is a more formalized management approach which (if you are being an MBA nerd) can be analyzed and quantified via Six Sigma (so some say ) through statistical analysis. When done right, these things really can be helpful (I am a huge believer in analysis tools and modeling) but, be warned, this stuff is often used in the world of McKinsey buzzword bullshit. Really, it's mostly common sense stuff with some models, tools and proven techniques.
Over simplified, one would employ concepts of Kaizen to ensure continual improvement all aspects of performance by evaluating problems and solving them, one would use Lean practices to reduce all unnecessary waste (time, money, manpower, materials) from specific processes (e.g. manufacturing) and one would use well defined analysis tools to quantify performance and provide feedback as to where attention should be focused.