Update README.md and replace .NET Cores with .NET (dotnet#97197)

* Update README.md and replace .NET Cores with .NET

* Apply suggestions from code review

---------

Co-authored-by: Jan Kotas <[email protected]>

README.md

@@ -36,13 +36,13 @@ We welcome contributions! Many people all over the world have helped make this p
 
 * [Contributing](CONTRIBUTING.md) explains what kinds of contributions we welcome
 * [Workflow Instructions](docs/workflow/README.md) explains how to build and test
-* [Get Up and Running on .NET Core](docs/project/dogfooding.md) explains how to get nightly builds of the runtime and its libraries to test them in your own projects.
+* [Dogfooding .NET](docs/project/dogfooding.md) explains how to get nightly builds of the runtime and its libraries to test them in your own projects.
 
 ## Reporting security issues and security bugs
 
 Security issues and bugs should be reported privately, via email, to the Microsoft Security Response Center (MSRC) <[email protected]>. You should receive a response within 24 hours. If for some reason you do not, please follow up via email to ensure we received your original message. Further information, including the MSRC PGP key, can be found in the [Security TechCenter](https://www.microsoft.com/msrc/faqs-report-an-issue). You can also find these instructions in this repo's [Security doc](SECURITY.md).
 
-Also see info about related [Microsoft .NET Core and ASP.NET Core Bug Bounty Program](https://www.microsoft.com/msrc/bounty-dot-net-core).
+Also see info about related [Microsoft .NET Bounty Program](https://www.microsoft.com/msrc/bounty-dot-net-core).
 
 ## Filing issues
 
@@ -52,7 +52,7 @@ For other issues, please file them to their appropriate sibling repos. We have l
 
 ## Useful Links
 
-* [.NET Core source index](https://source.dot.net) / [.NET Framework source index](https://referencesource.microsoft.com)
+* [.NET source index](https://source.dot.net) / [.NET Framework source index](https://referencesource.microsoft.com)
 * [API Reference docs](https://docs.microsoft.com/dotnet/api)
 * [.NET API Catalog](https://apisof.net) (incl. APIs from daily builds and API usage info)
 * [API docs writing guidelines](https://github.com/dotnet/dotnet-api-docs/wiki) - useful when writing /// comments