Actionscript and Java are two very different things - you can't really compare them too logically. Do some reading up if you want to understand the full differences, but let's just say actionscript is a scripting language mainly used for flash work, and Java is a fully fledged programming language that can code everything from small applets to enterprise level applications.
Chances are you don't have the JDK installed at school, but just the JRE - the JRE is the standard runtime environment nearly everyone has installed (since you need it to run Java apps.) On the other hand, the JDK is the development kit containing the compiler and suchlike that you need to build Java programs. If there's no use for it, they won't have installed it. Head over to C:\program files\Java (or wherever Java is installed) and search for a folder starting with jdk (not jre), if it's not there then you don't have it.
What you can do if you want to develop at school is download the JDK at home, copy the entire prorgam files folder onto a pendrive and then run javac from there. Haven't tried it personally, but it might work.
Incidentally, how long is Greenfoot taking to download?! It does it in a few seconds for me!