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 compiled language is one where the program, once compiled, is expressed in the instructions of the target machine. For example, an addition "+" operation in your source code could be translated directly to the "ADD" instruction in machine code.
An interpreted language is one where the instructions are not directly executed by the target machine, but instead read and executed by some other program (which normally is written in the language of the native machine). For example, the same "+" operation would be recognised by the interpreter at run time, which would then call its own "add(a,b)" function with the appropriate arguments, which would then execute the machine code "ADD" instruction.
You can do anything that you can do in an interpreted language in a compiled language and vice-versa - they are both Turing complete. Both however have advantages and disadvantages for implementation and use.
I'm going to completely generalise (purists forgive me!) but, roughly, here are the advantages of compiled languages:

Faster performance by directly using the native code of the target machine
Opportunity to apply quite powerful optimisations during the compile stage

And here are the advantages of interpreted languages:

Easier to implement (writing good compilers is very hard!!)
No need to run a compilation stage: can execute code directly "on the fly"
Can be more convenient for dynamic languages

Note that modern techniques such as bytecode compilation add some extra complexity - what happens here is that the compiler targets a "virtual machine" which is not the same as the underlying hardware. These virtual machine instructions can then be compiled again at a later stage to get native code (e.g. as done by the Java JVM JIT compiler).
Compiled vs. Interpreted Languages