What do you call moving a word to change a sentence's meaning?

Prosodic stress is stressing different words to change meaning:

I didn't take the test yesterday. (Somebody else did.)
I didn't take the test yesterday. (I did not take it.)
I didn't take the test yesterday. (I did something else with it.)
I didn't take the test yesterday. (I took a different one.)
I didn't take the test yesterday. (I took something else.)
I didn't take the test yesterday. (I took it some other day.)

Is there also a name or phrase describing changing the same word's position to change meaning?

ONLY she told me that she loved me. (She's the only one.)
She ONLY told me that she loved me. (She told me nothing more.)
She told ONLY me that she loved me. (She told no one else.)
She told me ONLY that she loved me. (She told me nothing else.)
She told me that ONLY she loved me. (No one else does.)
She told me that she ONLY loved me. (And nothing else.)
She told me that she loved ONLY me. (And no one else.)

Solution 1:

No. There isn't. It wouldn't be useful. There are too many ways to move words around, some of which change meaning, some of which don't. In fact, moving words around is a good description of a large part of Syntax.

For instance, in your second list above, the quantifier only is placed in successively later positions in the sentence, and its interpretation varies, according to its position, and according to syntactic rules. This is a well-known phenomenon, and in fact a pretty common lecture topic in linguistics classes.

Here's an old lecture about how it works. The key word is Constituent. The most basic principle of syntax is that Syntactic Rules Apply Only to Constituents. And never to chunks of language that don't form constituents.