Q:

What exactly is groovy-sql and are there other modules like it?

It's a .jar available in various versions at Maven Repo.
But what category is it? It is published by org.codehaus.groovy, the same outfit that I get my groovy-all dependency from. I also find that import groovy.sql doesn't work in a script unless I specifically include this dependency. So it would appear not to be part of the core language.  
Outside a Gradle context I find that I have to manually put the .jar file under ~/.groovy/lib in order to use it. If I put the wrong version (e.g. 2.5.9 for 3.0.2) under ~/.groovy/lib the script won't run... even if I'm not using groovy.sql at all!
Is this a "dependency"? It seems a typically powerful and hassle-free Groovy way of manipulating databases. Are there any other powerful add-on (non-core) Groovy .jar file modules like this, which have to be manually placed under ~/.groovy/lib, that I should know about?

A:

groovy consists of subprojects: 

https://github.com/apache/groovy/tree/master/subprojects

and groovy-sql one of the subprojects
all subprojects are published in maven as separate libraries
prior to version 2.5 there was groovy-all-XX.jar that includes all other groovy libraries

https://repo1.maven.org/maven2/org/codehaus/groovy/groovy-all/2.4.19/

however starting from v 2.5 groovy-all represented by groovy-all-XX.pom that depends on all other groovy libraries

https://repo1.maven.org/maven2/org/codehaus/groovy/groovy-all/2.5.0/

so, to include all groovy features you have to specify groovy-all in your maven/gradle/... dependency
and finally useful site to dig dependencies:

https://mvnrepository.com/artifact/org.codehaus.groovy/groovy-all/3.0.2

