Unlike waterfall, the gist of agile basically is that “every project must be aligned to clearly defined business goals and must focus on the early delivery of products that provide real added value to the business organization,” according to Henny Portman in their article on agile methodologies.
Agile development can use one of 50+ known agile approaches and frameworks, including the very popular Scrum (for which scrum teams might use a specific Scrum tool), its cousin Kanban, or other practices like Extreme Programming (XP), and Feature Driven Development (FDD).
Agile frameworks are adapted and hybridized—there’s no one right way to be agile. Whatever version you follow, you’re working with the basic principles laid out in the agile manifesto, focusing on communication, collaboration, self-organization, and responding quickly to new information.