I'm having a hard time classifying software development methodologies. In my understanding, SDLC is the overarching model used for software development approaches. SDLC methodologies can range from being very linear (e.g. the waterfall methodology) to being very adaptable (e.g. agile methodologies). Is this correct, i.e. do agile methodologies fall within the SDLC model?\
"Agile" isn't a methodology; it's a set of principles espoused by the Agile Manifesto. SDLC is an ambiguous term that can refer to a specific, waterfall-like methodology or a generic lifecycle. Either way, frameworks like Scrum or Kanban are more usefully classified as project management methodologies rather than lifecycles.
Frameworks Aren't Lifecycles
You could certainly make the case that agile methodologies are part of a systems- or software-development lifecycle. However, the converse is not true, since a framework or methodology isn't really a complete subset of a lifecycle.
For project management purposes, it is often useful to think of the lifecycle as a process that starts with project inception and flows through to project closure. A more systems-centric view might look at the lifecycle from development through deployment, and then ultimately to decommissioning; however, this is rarely encompassed within a single monolithic project, and is probably the wrong viewpoint for the typical project management professional.
Your mileage may vary.