What is the difference between Agile and Scrum?

What is the difference between Agile and Scrum? Is Agile a Methodology? Is Scrum a Methodology? 

Here is a quick answer:
No, Agile is NOT a Methodology. Scrum is NOT a Methodology either.
Scrum is a framework with a set of events, accountabilities, and a structure that facilitates the creation of value through adaptive solutions for complex problems, employing empiricism and lean thinking. Scrum has been in use since the early 1990s. On the other hand, 'Agile' is a set of four values and twelve principles documented in the 'Manifesto for Agile Software Development,' established in 2001. These values and principles were distilled from 'light-weight methods,' such as XP and Scrum. As a result, you will find the values and principles outlined in the 'Agile' manifesto reflected in the Scrum Framework.

Scrum: The Lightweight Framework for Product Development (not a methodology)
History of Scrum: 
The Scrum framework was originally co-presented by Ken Schwaber and Jeff Sutherland at the OOPSLA Conference in 1995. This framework was born from their accumulated knowledge and experiences, crystallizing the first formal definition of Scrum.

At its core, Scrum is a lightweight framework designed to facilitate value generation through adaptive solutions for intricate challenges. Guided by empiricism and lean thinking, Scrum acknowledges that knowledge stems from experience and decisions founded on observations. Lean thinking, a cornerstone of Scrum, revolves around minimizing waste and concentrating on essentials.
The Scrum framework uses an iterative and incremental approach for complex product development.

Agile: Values and Principles for Modern Development

The term "Agile" stands and references the set of values and principles formulated and documented on on February 11-13, 2001 as the Manifesto for Agile Software Development.

The 17 individuals who were part of larger set of people around the world who were using XP, Scrum etc, which was collectively called “light-weight methods. These innovators were “uncovering a better ways to develop software” at a time when the norm was the use of cumbersome, time-consuming heavy-weight methodologies. These inflexible approaches often hindered adaptability and made the process of changing or adjusting the product challenging.

In a rapidly evolving world, attempting to construct a complex product using rigid methodologies, which mandated exhaustive upfront planning and strict adherence to that plan, proved illogical. The dynamic nature of the environment called for flexible 'light-weight' methods that could accommodate change. Such adaptable methods embraced evolving requirements and simplified responses to changes, contrasting with the predetermined rigidity of established plans.
Furthermore, these methodologies shifted the paradigm by recognizing individuals as unique entities, as opposed to interchangeable 'resources' within a hierarchical and bureaucratic system."

The manifesto's roots extend from Scrum and various other processes recognized as "lightweight methods," including XP (eXtreme Programming), DSDM, Adaptive Software Development, Crystal, Feature-Driven Development, and Pragmatic Programming.

The Manifesto for Agile Software Development distills the core ideals of agility from these ‘light-weight methods’. Martin Fowler's poignant words—"We decide to use the term agile to describe this new breed of agile methods"—underscore the novelty and significance of this movement. You may find more of Martin Fowler’s account on his article titled “Writing The Agile Manifesto”

Jim Highsmith's account of the events leading to the manifesto's creation paints a vivid picture. You may find his account on his article titled “History of AgileManifesto”
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Further Reading:
History of AgileManifesto by Jim Highsmith

Writing The Agile Manifesto by Martin Fowler