Not everyone does this.
> The only difference really is who it's directed to, whether we've voiced it or wrote it down, and whether we self-censored some of it in the process.
That last part is the part that's key to computational thinking. What has been elided from your thoughts (expressed as an inner monologue, communicated via writing or voice to others)? Computational thinking requires you to be able to provide sufficient detail that a "computer" can repeat the process that you have performed, and potentially enough logical information that it can handle exceptional cases and situations. For a sufficiently advanced computer (read: intelligent and educated human), "Solve the equation for X" may be sufficient. For a program in C, you'll have to provide more detail. For a Mathematica program, it's about the same as communicating it to a human (depending on their level of education and the qualities of the equation, Mathematica may require more or less detail).