Swagger is tooling and rules for writing RESTful APIs. It includes a browser based editor, a UI to visualize OpenAPI in an interface, and a "Codegen" to generate server stubs and client libraries. These tools are basically everything you could need to write and implement an OpenAPI file. This is done to get everyone in the industry to be able to understand your API, using their framework. When I say everyone I mean everyone; computers, humans, developers, and non developers. It is a great way to create a highly consumable API.
Swagger is designed around OpenAPI, which provides a standardized API format to unify the use of RESTful APIs in the industry. OpenAPI is just the open source (hence the "Open") format they use to standardize everything. It was formerly know as Swagger Specification but broke away from Swagger into its own company to become OpenAPI 3.0.