Here is a quick software development methodology cheat sheet.
Note: There are many specific processes defined for some of the methodologies that are beyond the scope of this article. The main goal of this article is to give very high-level definitions of each methodology.
Waterfall - You do ALL of one phase, then ALL of the next, then ALL the next (eg. design -> coding -> testing).
Agile - Agile is a philosophy, not a step-by-step methodology1. It is a set of attitudes about software development with the goal of improving communication and the overall development process for all parties involved. You are "agile" if you align yourself with the agile philosophy and make your actions in development reflective of that.
Scrum - A template of steps to follow for the development cycle. It is an implementation of agile- it is supposed to follow the principles and attitudes of the agile philosophy. At the same time, it actually gives you the steps that you can follow. In this methodology, you have a prioritized todo list, and you incrementally and iteratively complete chunks of the todo list. By performing incremental and iterative development, you allow requirements to be flexible and changeable since you are not commiting to completing one entire phase before moving to another one (waterfall). Thus, the development process can better cope with inevitable changes.
Extreme Programming (XP) - XP is a methodology which implements a set of rules that you follow to optimize software development and make it easier to collaborate and work with a team while sustaining a high level of software quality. XP is an agile methodology as it aligns with agile principles.
Kanban - A software development process that aims to manage the flow of items being worked on (for example, the flow of completion of each item on the project's todo list). Kanban processes seek to identify and eliminate bottlenecks in the software development lifecycle.
Lean - Product development principles that have been translated to the software development domain from lean manufacturing. There are 7 principles- eliminate waste, build in quality, create knowledge, defer commitment, deliver quickly, respect people, and optimize the whole.
Cowboy Coding - Developers have complete control of software development. There is no formal structure that guides the project along. The easiest way to think of this is as a "free for all" where you can do whatever part of the project you want whenever you want.
Iterative Development - The software is built knowing that future versions (iterations) will be used to refine the project.
Incremental Development - A software project is divided into chunks and each chunk is developed by the team, one at a time.
No Silver Bullet - A paper written in 1986 by Fred Brooks, in which he argues that "there is no single development, in either technology or management technique, which by itself promises even one order of magnitude improvement in productivity, in reliability, in simplicity."
Let me know if I've missed anything and I'll put it up!
In the real world, a lot of people mix up agile and scrum. Sometimes they mix up agile and some other completely unrelated methodology. Just remember that agile is the philosophy, scrum is a methodology, and people will probably get them mixed up. ↩