There is a large group in the IT community, regardless of whether Scrum / Agile / non-Agile who seem to be confused with this matter: They use Scrum and Agile interchangably. Unfortunately, even thought leaders in the Scrum community propagate this misunderstanding.
Time and again, we can hear people state: "Oh we tried Agile a couple years ago. Didn't help much, we went back to Waterfall." Upon further inquiry, we find out they did Scrum, but neither understood nor embraced the Agile Manifesto. Usually, that is combined with a failure to be cross-functional, to apply solid Engineering Practices and to let go of ineffective organizational habits.
So then, what is Scrum?Before I go into details, let me clear up one thing: Scrum is part of the agile community and therefore qualifies as an agile framework. However, neither is Scrum representative of all agile methods - nor does applying Scrum in your organization automatically mean you're agile.
Why being Agile doesn't mean you do Scrum.This one goes down two streams:
You can't simply interchange the words "Scrum" and "Agile"First, there is a huge difference between an equivalence (A <==> B) and an implication (A ==> B). In logic, we typically use this analogy: "When it rains, the street is wet. The street is wet: Did it rain? - No, maybe someone poured a bucket of water or a lawn sprinkler went rampant."
You can apply this for Scrum and agility as well. When you do good(!) Scrum, you are agile. The reverse, however, is not true. For example, as stated in the Post-Scrum Manifesto, even when you started with Scrum, your Scrum should evolve over time until it doesn't even resemble Scrum any more.
Agile teams don't necessarily use ScrumTruly agile teams are doing highly effective work and deliver great results, but chances are - they're not doing Scrum.
Maybe they did Scrum at one time, but maybe they also started with a different agile framework like XP, Lean, Design Thinking, Crystal, DAD, DSDM - or simply evolved whatever way of working they started with. Chances are they are agile and haven't even heard of Scrum - albeit the odds are quite low, given how widely spread Scrum is today.
Why doing Scrum doesn't mean you're AgileLet's start with linguistics here: You do Scrum, but you are agile. You can't be Scrum or do Agile.
Scrum (mis-)understood as a processUnfortunately, there is a wide spread misunderstanding that Scrum is a "method" or "process". Many consultants, trainers and managers fail to properly discern the consequences of merely applying Scrum as a process. The result is always the same: Scrum is being applied as a Cargo Cult, doing everything exactly as prescribed, but not reaping any benefit. This is the problem with frameworks: They only serve as a yardstick, you still need to fill them with life by yourself. Failure to actually change structures and behaviours inside and around Scrum will result in product/project failure.
There is a weak relationship between Scrum and the Agile Manifesto
There is no reference in the Agile Manifesto to Scrum. In fact, only the signatures of Jeff Sutherland and Ken Schwaber correlate the Manifesto with Scrum. It's not the Scrum Manifesto: Jeff and Ken were two of 17 contributors, implying that Scrum only accounts for roughly 10% of agility.
Vice versa, Scrum does not primarily focus on agility. The Agile Manifesto is typically just a "Must-Have" module in a Scrum training - but just one small block. You're lucky if your trainer sponsors more than an hour for the Manifesto. The Agile Principles are sometimes even skipped in Scrum classes. Agility makes up less than 10% of a Scrum course, making the relationship inherently weak from the outset.
Scrum without agile principles
Most people practice Scrum without taking heed of the Agile principles. Even if they know about them somewhere back in the recesses of their mind, they do not consciously work to conform the organization towards agile principles. Much rather, they use their organization as an excuse for circumvening these principles.
However, a "principle" is not a recommendation for something you could do, but a "law" - similar to gravity: It applies even when you don't like it. Scrum can be implemented within an organization in complete disregard of Agile principles, although it should not.
So then, what is Agile?
While Scrum is fairly easy to comprehensively explain, agility is much harder to explain. Based on my knowledge, to this point, the agile community has yet not found an accurate, comprehensive description of what "being agile" really means, beyond applying the values and heeding the principles of the Manifesto.
Probably the most adequate description of "agile" is: A mindset of Continuous Improvement and Customer Value Orientation. A consequence of being agile is that no method, no process, no piece of information is sacred - everything is up for scrutiny, inspection, change and possibly complete discarding when a better path becomes known: Even the mindset itself.
ConclusionYou are free to do Scrum in your organization without being agile. You can find many quacks and snake oil sellers who will gladly support you with that. But it's setting up for failure.
Likewise, you can be completely agile without doing anything that even remotely resembles Scrum. In fact, that's what is naturally going to happen once you pursue down the agile road.
Therefore, you should never confuse "doing Scrum" with "being agile".