From Microsoft's docs about ADO.NET
ADO.NET is a set of classes that expose data access services for .NET Framework programmers. ADO.NET provides a rich set of components for creating distributed, data-sharing applications. It is an integral part of the .NET Framework, providing access to relational, XML, and application data. ADO.NET supports a variety of development needs, including the creation of front-end database clients and middle-tier business objects used by applications, tools, languages, or Internet browsers.
From Npgsql's docs
Npgsql is an open source ADO.NET Data Provider for PostgreSQL, it allows programs written in C#, Visual Basic, F# to access the PostgreSQL database server. It is implemented in 100% C# code, is free and is open source.
In addition, providers have been written for Entity Framework Core and for Entity Framework 6.x.
What's a data provider? I think the one of the best answers come from the Wikipedia article about ADO.Net Data Providers:
An ADO.NET data provider is a software component that interacts with a data source. ADO.NET data providers are analogous to ODBC drivers, JDBC drivers, and OLE DB providers.
ADO.NET providers can be created to access such simple data stores as a text file and spreadsheet, through to such complex databases as Oracle Database, Microsoft SQL Server, MySQL, PostgreSQL, SQLite, IBM DB2, Sybase ASE, and many others. They can also provide access to hierarchical data stores such as email systems.
So I wouldn't say that Npgsql is not a subset of ADO.Net. It is, to some extent, a piece of software containing a collection of classes that implement a certain number of standard interfaces; which will be the ones considered "essential to every data provider" and a few of the "optional ones". You should take a look as well to ADO.NET Architecture