What is difference between Snowflake Database And Snowflake Schema

The two concepts confused me a lot recently.

Snowflake Database more refers to the data service and its website address as below:

https://www.snowflake.com/

This is more like a data platform or data warehouse on the cloud that provides SQL engine functionalities.

On the other hand, Snowflake schema is more like an algorithm that design database schema.

Are they totally two different things and just have the same name coincidently?

Databases and schemas are used to organize data stored in Snowflake:

• A database is a logical grouping of schemas. Each database belongs to a single Snowflake account.
• A schema is a logical grouping of database objects (tables, views, etc.). Each schema belongs to a single database.

Together, a database and schema comprise a namespace in Snowflake.

Source: https://docs.snowflake.com/en/sql-reference/ddl-database.html