Q:

How does 'distorting an argument' differ from 'changing the subject'?

Source: 
pp 137-138, A Concise Introduction to Logic (12 Ed, 2014) by Patrick J. Hurley

The red herring fallacy can be confused with the straw man fallacy because both have
  the effect of drawing the reader/listener off the track. This confusion can usually be
  avoided by remembering the unique ways in which they accomplish this purpose.
  In the straw man, the arguer begins by distorting an opponent’s argument and concludes by
  knocking down the distorted argument.
  In the red herring, the arguer ignores the opponent’s
  argument (if there is one) and subtly changes the subject.
  Thus, to distinguish the
  two fallacies, one should attempt to determine whether the arguer has knocked down
  a distorted argument or simply changed the subject. Also keep in mind that straw man
  always involves two arguers, at least implicitly, whereas a red herring often does not.

I do not comprehend the distinction in the bolded (subordinate) clause. To me, the bolded seems only to use different words to  describe the same error; ie: how can you distort an argument without changing the subject, and vice versa? What have I neglected? 

A:

"Distorting the argument" is synonymous with a strawman whereas red herring and changing the subject are synonymous. In the former, one misunderstands the argument offered and argues against something not suggested. In the latter, one distracts from the potential argument and says something else.
One problem with any examples is that both of these fallacies are informal (See this post), which means people will disagree about whether they fit or not.
I'll start with a distortion ("strawman") example:
Sample Argument A

If we let terrorists into the country, then they will hurt people here.
We do not want people here to get hurt.
Therefore we shouldn't let terrorists into the country.

A distorted response to sample argument A is to transform it and critique the transformed version. For example:

I can't believe you said that. How can you say that muslims will hurt people here? That's absurd. We should never limit immigration.

The problem is that Argument A claim #1 does not say "muslims", it says "terrorists". If you want to prove you're not arguing a strawman by suggesting muslim immigration to your country should be limited, you're going to have to do a lot of legwork to connect the dots. (again, this is an informal fallacy so people could disagree about whether such legwork is even possible -- but it's quite evident the initial maneuver is distorting the initial claim).
A distracting response to the same argument would go something like this:

It's important to realize that terrorism has many causes -- like global warming (aside: or so argued Bernie Sanders?)

This has nothing to do (at least immediately) with whether we should let terrorists immigrate. (Again, work could be done to make it less fallacious, tying in how we have an obligation to those we harm, etc., but as written it's a completely disjointed fact designed to draw our attention).

