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FoalTS and NestJS are both Node.js frameworks that support TypeScript natively. They have some differences though:
NestJS architecture is greatly inspired by Angular. Foal's architecture is meant to be simpler and easily approachable from non-Angular developers. You'll only find three "components" in Foal: controllers, services and hooks. The goal is to give more freedom to developers. They don't spend time trying to understand how the framework wants them doing what they want to do. Instead, the framework lets them build their app in their own way.
FoalTS is also more than a TypeScript framework. Not only does it bring architecture. But it also offers many dev tools and utils out-of-the-box useful in many scenarios. For example, in FoalTS, you have utils to hash passwords, validate and sanitize request bodies, control access through groups and permissions, write and run unit tests, generate database migrations or manage configuration variables between several environments.