Agile is a mindset. It does not mandate processes. It is not prescriptive. Neither are many of the tools that are commonly associated to it. Neither is Lean, another mindset mistakenly named as Agile, whose boundaries continue to fade and fusion, at least in the software world.
Agile aims for simplicity and focusing on objectives rather than the process to get there. It is supposed to bring freedom and focus as it shortens the feedback loop and looks for no blame but the next step or alternatives. In that sense, Agile strives for reducing complexity of any problem. Traditionally on a software context, where it was born, but expandable to other fields if you remember to use only the essentials. Agile is about getting iterating and increment.Evolving a product. Think on a bike that became a motorcycle. Think about a carriage that transformed into cars and how cars have been transforming since the first unit by Karl Benz in 1886. In software you recognize them from XP and Scrum.
Lean looks for reducing waste and keeping a state of flow. In commoners language, we do only what is required, that we know is required and keep the focus in completing that before taking on a new challenge. Think about how a house is built. You have foundation, framing and slowly fill in layers until you can turn on a light and move into it. Several layers added to a same final product. Even though it was born on engineering/assembly lines, much of it applies to software. In this you might have heard of Kanban.
Lean and Agile approaches are complimentary. None is about being imprecise, hasty or incomplete. Both are about placing stepping stones, making informed decisions based on what you know now.
I would argue the purple intersection is much bigger, almost eclipsing the differences, which I do believe lie mostly in details; they are not irreconcilable.
Again, it is not uncommon to see references that blurry the lines of this intersection. For intellectual and learning purposes it is always good to remember the boundaries, but once they are learned and applied they shift our mindset and introduce tools that are more often than not compatible (Kanban board vs Scrum board anyone?). And that is why I find their differences can become less relevant.
That is what I mean by Agile. What do you mean by Agile?