I'm trying to get a better understanding of the difference. I've found a lot of explanations online, but they tend towards the abstract differences rather than the practical implications.
Most of my programming experiences has been with CPython (dynamic, interpreted), and Java (static, compiled). However, I understand that there are other kinds of interpreted and compiled languages. Aside from the fact that executable files can be distributed from programs written in compiled languages, are there any advantages/disadvantages to each type? Oftentimes, I hear people arguing that interpreted languages can be used interactively, but I believe that compiled languages can have interactive implementations as well, correct?
A language itself is neither compiled nor interpreted, only a specific implementation of a language is.  Java is a perfect example.  There is a bytecode-based platform (the JVM), a native compiler (gcj) and an interpeter for a superset of Java (bsh).  So what is Java now? Bytecode-compiled, native-compiled or interpreted?  
Other languages, which are compiled as well as interpreted, are Scala, Haskell or Ocaml.  Each of these languages has an interactive interpreter, as well as a compiler to byte-code or native machine code.
So generally categorizing languages by "compiled" and "interpreted" doesn't make much sense.
Compiled vs. Interpreted Languages