The biggest difference between the two cycles happens after those first two steps. In the business agility cycle we then decide-communicate-act, suggesting that it is the higher-ups who make and communicate the decisions and the lower-end of the organizational food chain (the "worker bees") that execute the organization's strategic solution.
If that seems a bit command-and-control, its because it is (a bit). It's also likely necessary in larger organizations where it is virtually impossible to avoid having 2 or more layers of management. There, the "communicate & act" steps are really the process of providing focus, and communicating objectives and constraints to the knowledge workers, and letting them apply principles of collaboration and self-organization to solve the problem (like in the software-agility cycle).
So the key difference between business-agility and software-agility is the extra emphasis of the latter on "the people factor" and on the notion of dynamic self-organization of knowledge-workers as empowered, self-organizing teams. This difference between agility at the business-level versus software-level is also the key difference between Lean-vs-Agile:
- Lean focuses more on flow whereas Agility focuses more on adapting to change (this is true of both software agility and business-agility). As it turns out, focusing on flow requires being able to adapt to change; and focusing on adaptiveness and responsiveness requires a focus on flow. So here, the end-results may be quite similar
- Agile software development emphasizes a very hands-off management style of not just trusting and empowering the team(s), but often to the extreme of basically saying "leave us alone and don't interfere" to management (and in return promising extreme transparency and frequent tangible end-results).
- Much of this is due to the fact that the scope of Agile development is limited to software projects and teams, whereas Lean is targeted at enterprise-wide scale across the whole value-stream.
That is not to say that Lean (or business-agility) don't emphasize trusting and empowering workers and teams (they do). But they don't have the underlying inherent attitude of "just trust us and stay out of the way." The "trust" often doesn't seem to extend as far in the other direction with Agile development (e.g. not trusting management direction to the same extent that management is asked to trust the team).
I think this stems from the fact that software agility started more at the grass-roots level, with developers and teams struggling to create good, quality software in the face of what was all too often a fundamentally broken management framework for the governance, visibility, and lifecycle of software development projects. Because they were working and trying to get support from the bottom-up, they needed to be shielded from and unshackled by all the dilbert-esque "pointy haired managers" and their big, bad governance framework with its "evil" waterfall lifecycle.
And in that context, the advice of "just get out of the way and trust us and we promise to deliver working software every 2-4 weeks" is actually a very effective strategy to employ. When management doesn't "get it", their attempts to steer, direct and intervene are often the equivalent of "friendly fire" (which, despite well intentions, still yields calamitous results.)
But Lean comes from a history of a much more enterprise-wide scope, often even using a top-down deployment strategy. So when it asks management to trust and empower workers and teams it expects the corresponding change in its leaders and their leadership-style, and for them to still play a strong, active and participative role with their projects and teams.
Agile teams often get a "bad rap" for having this isolationist attitude toward management. And sometimes that "rap" is warranted. But when the leadership "gets it" and understands and values the "new" paradigm of why+how agile works, and why+how the "old way" didn't, then it probably is time for the leadership to play a different, more active role while still trusting and empowering teams (and still enabling self-organization). This is the view that Lean takes toward management, and is a big part of why it is better received by management and is more broadly applicable for scaling agility "up" and "out" in larger enterprises.