It seems there is good potential for confusion unless we use the same terms consistently when discussing architecture and design across teams.
Even the term RDS (Relational Database Service) is sometimes said to be inaccurate since it is a "Relational Database SERVER as a Service"
A few related terms that cause confusion:
"Schema" could refer to a Database Schema or in some contexts, a single table's logical data structure. (Or a single data set's data structure -- or a standard for one, like JSON Schema)
Data Catalog products like "AWS Glue Data Catalog" which only store the metadata or schemas of the table they crawl ... refer to the entities they store as "Databases" and "Tables" (but no "Schemas") and documentation includes guides talk about "creating a database" and "creating a table" in AWS Glue. There has to be a better way to refer to all these entities without using the word schema with so many meanings -- or calling both physical tables and their metadata as "tables". Otherwise this is needlessly confusing and had for beginners.
https://docs.aws.amazon.com/glue/latest/dg/define-database.h...
https://docs.aws.amazon.com/glue/latest/dg/tables-described....
As to schema itself, yes, it’s heavily overloaded, and you just to grok it from context. I can talk about a table’s schema or a DB’s schema, or as you mentioned, JSON schema. Although the latter is helped by simply not using JSON in a relational DB.
You must remember that SQL is an ancient language, and the relational model is even older. There are going to be oddities.