What is the difference between allprojects and subprojects

In a multi-project gradle build, you have a rootProject and the subprojects. The combination of both is allprojects. The rootProject is where the build is starting from. A common pattern is a rootProject has no code and the subprojects are java projects. In which case, you apply the java plugin to only the subprojects:

subprojects {
    apply plugin: 'java'
} 

This would be equivalent to a maven aggregate pom project that just builds the sub-modules.

Concerning the two syntaxes, they do the exact same thing. The first one just looks better.