The term serverless framework can refer to two different things: the general concept of a development framework for deploying code to serverless platforms such as AWS Lambda, or one specific such framework that is branded as Serverless Framework, developed by Serverless, Inc.
Broadly, a serverless framework is a software development tool that’s aimed at making it easier for developers to deploy code to serverless cloud platforms.
Typically, a serverless framework will exist for one or more programming languages, and be aimed at helping with deployment to one or more cloud serverless platforms. Zappa, for example, is an open source serverless framework designed to facilitate deploying Python applications to AWS Lambda.
Serverless, Inc.’s Serverless Framework is one example of a serverless framework as defined above: it’s a development tool that facilitates deploying apps written in a variety of different coding languages to AWS Lambda (among other platforms).