Difference between agile and iterative and incremental development

• Iterative - you don't finish a feature in one go. You are in a code >> get feedback >> code >> ... cycle. You keep iterating till done.
• Incremental - you build as much as you need right now. You don't over-engineer or add flexibility unless the need is proven. When the need arises, you build on top of whatever already exists. (Note: differs from iterative in that you're adding new things.. vs refining something).
• Agile - you are agile if you value the same things as listed in the agile manifesto. It also means that there is no standard template or checklist or procedure to "do agile". It doesn't overspecify.. it just states that you can use whatever practices you need to "be agile". Scrum, XP, Kanban are some of the more prescriptive 'agile' methodologies because they share the same set of values. Continuous and early feedback, frequent releases/demos, evolve design, etc.. hence they can be iterative and incremental.

Iterative development implies revisiting usual waterfall model steps over the course of product lifetime. The stages can even overlap, i.e. while doing end-to-end testing you could already start preparing new requirements.

Incremental development means you roadmap your features and implement them incrementally.

Agile aims at creating "potentially shippable product" after every sprint. How you achieve it is a different story. Agile tries to employ "best" techniques from various fields (e.g. extreme programming). Agile does not exclude running neither incremental nor iterative development.

Incremental development means that different parts of a software project are continuously integrated into the whole, instead of a monolithic approach where all the different parts are assembled in one or a few milestones of the project.

Iterative means that once a first version of a component is complete it is tested, reviewed and the results are almost immediately transformed into a new version (iteration) of this component.

So as a first result: iterative development doesn't need to be incremental and vice versa, but these methods are a good fit.

Agile development aims to reduce massive planing overhead in software projects to allow fast reactions to change e.g. in customer wishes. Incremental and iterative development are almost always part of an agile development strategy. There are several approaches to Agile development (e.g. scrum).