Each of those words has a character of its own. It not only denotes something (that is, to serve as the word “for” something) but connotes, or implies, some other things. A cur is not man’s best friend, for example, even though both denote some king of dog.

In addition, each of these words has, to go back to the woodworking metaphor, a particular sound that it makes, a particular face that it makes you make, when you say it. A currrrrrrr literally makes you make an angrier, growlier face than straaaaaay, which almost makes your face smile. (Check a mirror.)

The words also have lengths: cur, stray, man’s best friend.

Your word choice here is the base level of material with which you build your story. You can treat the word sincerely, ironically, or with other tones–you can call a beautifully groomed Pomeranian a cur, for example.