<p>I see many different Java terms floating around.  I need to install the JDK 1.6.  It was my understanding that Java 6 == Java 1.6.  However, when I install Java SE 6, I get a JVM that reports as version 11.0!  Who can solve the madness?</p>

JDK - Java Development Kit
JRE - Java Runtime Environment
Java SE - Java Standard Edition
SE defines a set of capabilities and functionalities; there are more complex editions (Enterprise Edition – EE) and simpler ones (Micro Edition – ME – for mobile environments).
The JDK includes the compiler and other tools needed to develop Java applications; JRE does not.  So, to run a Java application someone else provides, you need JRE; to develop a Java application, you need JDK.
Edited
:
As Chris Marasti-Georg pointed out in a comment, you can find out lots of information at Sun's
Java
web site, and in particular from the
Java SE
section, (2nd option, Java SE Development Kit (JDK) 6 Update 10).
Edited 2011-04-06:
The world turns, and Java is now managed by Oracle, which bought Sun.  Later this year, the
```
sun.com
```
domain is supposed to go dark.  The new page (based on a redirect) is this
Java
page at the Oracle Tech Network.  (See also
java.com
.)
Edited 2013-01-11:
And the world keeps on turning (2012-12-21 notwithstanding), and lo and behold, JRE 6 is about to reach its end of support.
Oracle
says no more public updates to Java 6 after February 2013.
Within a given version of Java, this answer remains valid.  JDK is the Java Development Kit, JRE is the Java Runtime Environment, Java SE is the standard edition, and so on.  But the version 6 (1.6) is becoming antiquated.
Edited 2015-04-29:
And with another couple of revolutions around the sun, the time has come for the end of support for Java SE 7, too.  In April 2015, Oracle
affirmed
that it was no longer providing public updates to Java SE 7.  The tentative end of public updates for Java SE 8 is March 2017, but that end date is subject to change (later, not earlier).