Terminology

Postman: Desktop application to manage HTTP requests and responses, tests and data
newman: Command line tool that is able to run Postman tests defined in a Collections file
Postman collections: Is a file describing a set of HTTP tests and scripts executable in Postman. It is formatted as a JSON file

Postman features

Import OpenAPI (Swagger) files and generate collections of test cases. Usually the tests need some manual tuning to be run.
Collections contains the list of tests, the data exchanged and the test scripts before and after the HTTP call. More info here.
The tests scripts before and after the HTTP request/response are written in pure Javascript , with a basic API for JSON schema checks and other checks. Lacks (as far as we know) the capability to load schemas from external files.
The postman collections can be created importing OpenAPIs, but will need manual intervention using the Postman application to be finalized. When they are ready, they can be shared as a unique JSON file, to be imported in another instance of the application or to be run with the command line command newman or to be used with other tools (many API tools support them).

OpenAPIs from TM Forum use Postman collection as the core of their Compliance Test Kit (CTK)