Historically maybe-sorta; the consumer download for Java used to be called the JRE. It hasn't been updated since Java 8. .NET ships with a pretty full toolkit even on consumer systems (it's what undergirds PowerShell too) so .NET probably maps better to the whole-hog JDK.

The JRE-equivalent in the .NET stack is the Common Language Runtime. The JRE processes Java bytecode; the CLR processes Common Intermediate Language (CIL, formerly MSIL) instructions.