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?
The extreme and simple cases:

A compiler will produce a binary executable in the target machine's native executable format. This binary file contains all required resources except for system libraries; it's ready to run with no further preparation and processing and it runs like lightning because the code is the native code for the CPU on the target machine.
An interpreter will present the user with a prompt in a loop where he can enter statements or code, and upon hitting RUN or the equivalent the interpreter will examine, scan, parse and interpretatively execute each line until the program runs to a stopping point or an error. Because each line is treated on its own and the interpreter doesn't "learn" anything from having seen the line before, the effort of converting human-readable language to machine instructions is incurred every time for every line, so it's dog slow. On the bright side, the user can inspect and otherwise interact with his program in all kinds of ways: Changing variables, changing code, running in trace or debug modes... whatever.

With those out of the way, let me explain that life ain't so simple any more. For instance, 

Many interpreters will pre-compile the code they're given so the translation step doesn't have to be repeated again and again. 
Some compilers compile not to CPU-specific machine instructions but to bytecode, a kind of artificial machine code for a ficticious machine. This makes the compiled program a bit more portable, but requires a bytecode interpreter on every target system.
The bytecode interpreters (I'm looking at Java here) recently tend to re-compile the bytecode they get for the CPU of the target section just before execution (called JIT). To save time, this is often only done for code that runs often (hotspots).
Some systems that look and act like interpreters (Clojure, for instance) compile any code they get, immediately, but allow interactive access to the program's environment. That's basically the convenience of interpreters with the speed of binary compilation.
Some compilers don't really compile, they just pre-digest and compress code. I heard a while back that's how Perl works. So sometimes the compiler is just doing a bit of the work and most of it is still interpretation.

In the end, these days, interpreting vs. compiling is a trade-off, with time spent (once) compiling often being rewarded by better runtime performance, but an interpretative environment giving more opportunities for interaction. Compiling vs. interpreting is mostly a matter of how the work of "understanding" the program is divided up between different processes, and the line is a bit blurry these days as languages and products try to offer the best of both worlds.
Compiled vs. Interpreted Languages