Also, a lot of "classic" interpreters also include the lex/parse phase along with execution.
For example, consider executing a Python script. When you do that, you have all the costs associated with converting the program text in to the internal interpreter data structures, which are then executed.
Now contrast that with executing a compiled Python script, a .pyc file. Here, the lex and parse phase is done, and you have just the runtime of the inner interpreter.
But if you consider, say, a classic BASIC interpreter, these typically never store the raw text, rather they store a tokenized form and recreate the program text when you do "LIST". Here the byte code is much cruder (you don't really have a virtual machine here), but your execution gets to skip some of the text processing. That's all done when you enter the line and hit ENTER.