Exactly. These are fallacies that are constrained to arguments that are logical in nature. That is, the agreed upon rules of argument and discussion is to use logic. And most arguments even of your second or third category use elements of logic to help strengthen the argument.
However, not all arguments are meant to be or can be solved with pure logic. Otherwise we'd all be Kantians. People will intentionally argue using Appeal to Emotion or Slippery Slope and, within certain contexts, this can be perfectly fine. Just throwing around "That's a logical fallacy, therefore your argument is invalid" is the perfect example of Fallacy Fallacy.
Even worse, just relying on having a codex of fallacies to throw around into any context reduces most arguments into petty squabbles and making it too easy to dismiss your opposition. But for discussions of the second and third mode you need to engage the person and get to the root of their ideas and argue using the proper rules and context.
However, not all arguments are meant to be or can be solved with pure logic. Otherwise we'd all be Kantians. People will intentionally argue using Appeal to Emotion or Slippery Slope and, within certain contexts, this can be perfectly fine. Just throwing around "That's a logical fallacy, therefore your argument is invalid" is the perfect example of Fallacy Fallacy.
Even worse, just relying on having a codex of fallacies to throw around into any context reduces most arguments into petty squabbles and making it too easy to dismiss your opposition. But for discussions of the second and third mode you need to engage the person and get to the root of their ideas and argue using the proper rules and context.
My personal revelation of all of this came from reading this piece titled "You Baloney Detection Kit Sucks": http://plover.net/~bonds/bdksucks.html