As noted by Michael Petrotta in the question you reference, scripts are generally interpreted and slowish , programs are generally compiled and fasterish. Compiled is often faster than intepreted because interpretation includes compilation at run time (vague and not always the case, but good enough).
Scriptable, to me, means that the object in question supports the interfaces required to be accessable from one or more script languages (for example, JavaScript and/or VBScript).
Programmable, to me, means that the object in question supports the interfaces required to be accessable from a programming language (for example, C++ or Java).
Interpreted and Compiled languages are all programming languages so it is all programming.
Summary: Scriptable vs Programmable are two vaguely synonomous terms.