I noticed that Lean Kanban term appears quite frequently. I've tried to figure out what's the difference between Lean Kanban and Classic, but no success. Maybe someone dealt with both and could describe the difference and explain when to use what?
Lean is to Kanban as agile is to Scrum. One is a concrete implementation of the other.
Using the term "lean kanban" is just an attempt to court favour from Google/Bing for keyword density and is the result of copywriters rather than an actual thing.
All Kanban is Lean... But not all Lean is Kanban...
Kanban is a lean methodology focused on creating continuous flow of work while eliminating waste (muda) in the system. There is no difference between Kanban and Lean Kanban.
Where there are some differences however...
Kanban for software development differs slightly from the classic Lean Kanban formulated by Toyota in the 1980's and used in manufacturing environments.
Here's a good book that focuses on kanban for software development and gets into some of the nuances.
Kanban: Successful Evolutionary Change for Your Technology Business Paperback – April 7, 2010 by David J. Anderson (Author), Donald G Reinertsen (Foreword)
The basic processes, tools, and objectives of Kanban for software development remain unchanged (WIP, JIT, Slack, Pull Model, Cycle Time, SLA, Work Classes, Flow, Eliminate Waste, Visualize all work). However, how work is visualized on the Kanban board is a bit more flexible than in traditional kanban. Also not all work on a software kanban board is necessarily same sized or forced to be same sized.
Its also fairly common to see software teams using Kanban adopting practices from Scrum such as the daily standup, retrospective, Product Owner concept, etc. Some people call these types of teams "Scrumban" teams.
Kanban is a Lean tool, that's about it. There is no Kanban and Lean Kanban. The Kanban method was borrowed from Toyota's Production System (the creators of the Lean processes movement).
See below definition of Kanban:
“Kanban is the Japanese word for “card,” “ticket,” or “sign” and is a tool for managing the flow and production of materials in a Toyota-style “pull” production system.”
Excerpt From: by Jeffrey K. Liker. “The Toyota Way - 14 Management Principles from the World's Greatest Manufacturer @Team LiB.” iBooks.
So: Kanban + just in time + kaizen + a variety of other tools = Lean Methodology