"Unfortunately, [the terms] leaked into the documentation that everyone reads" - We did this on purpose to align everyone's terms. It makes things so much easier when the people asking and answering questions are using the same language.
"The official JSON Schema website has a validator you can try: https://www.jsonschemavalidator.net/" - Would have been better to point to the actual official JSON Schema website's tools page (https://json-schema.org/tools) that lists many online validators.
There are some interesting conceptions of OpenAPI in here as well. Specifically, OpenAPI isn't a JSON Schema document. It's its own kind of document that has JSON Schemas embedded in it.
Still, it's a decent high-level summary. If you're interested in diving a bit deeper, definitely come visit us in Slack (https://json-schema.org/slack).