First important point about Agile and Scrum is, that they both complement each other. Agile is a bigger picture and Scrum is one part or one flavour of it.
Scrum is one of the followers of Agile. Agile has many more flavours like Extreme programming, Lean, Kanban and Crystal. Scrum is one of it and known to be one of the lightweight agile frameworks. Due to its lightweight nature Scrum is very popular and believed to be comparatively easy to implement and follow. As said earlier, this makes Scrum one of the Agile Flavours.
Agile is based on iterative and incremental development which is implemented in Scrum by its methodology of roles, ceremonies and artifacts. Agile also emphasizes on time-boxing which is implemented in scrum beautifully by fixing times of its Sprints and Ceremonies. All the events/ceremonies in Scrum have fixed durations which are recommended for one month of Sprint. They can be adjusted for any increase or decrease, however we shall discuss all those events in detail further during this course. Scrum events are checkpoints for adaptation.
Agile talks about adaptation and Scrum implements it daily (Daily Scrum), End of Sprint (Sprint review), before next Sprint (Sprint Retrospective/planning) meetings. In a nutshell, Scrum is an implementer of agile methodology and used widespread due to its ease of implementation.