I am not sure if I got it right: java.base is the underlying base module from all other modules and contains all the base stuff from them, like a superclass from a class. And java.se is the module which contains the whole JDK, like a subclass (which contains the basic functionality and more specific stuff)
java.base is the base module; every other module implicitly or explicitly depends on it:
If the declaration of a module does not express a dependence on the
java.basemodule [...] then the module has an implicitly declared dependence on thejava.basemodule.
(Java Language Specification 17 §7.7.1)
java.se "defines the API of the Java SE Platform" (per documentation). It roughly (?) comprises all the classes which were present in Java SE before modularization, except being separated now in different modules, e.g. java.desktop or java.sql. It does not include JDK specific modules (such as jdk.javadoc). A Java runtime might not necessarily provide all of these modules; for example you could use jlink to create a Java runtime which only contains the modules you need (at the minimum java.base).
The Java API specification can also be helpful for understanding the content of modules and their relations:
Your comparison with a class (module java.base) and its subclass (module java.se) works in this case because java.se acts kind of like an 'aggregator' module which itself does not contain or export any packages but only has indirect exports through requires transitive. See this question for why the java.se module exists. Although normally you would not declare a dependency on java.se because that defeats the purpose of making custom small runtime images; instead you would only declare dependencies on the specific modules you really need, e.g. java.logging.
Such aggregator modules are rather uncommon though. In most cases modules will rather be used for grouping related packages, and restricting access to internal implementations. However, in these cases services defined by one module and the corresponding service provider being implemented and declared by another module are similar to your analogy.