At first blush, US 9083821 that you referred to seems to be a very good example of a software patent. I will therefore discuss a little about the patent and how it relates to the invention–implementation dichotomy. I've glossed over the precise details of the invention for simplicity's sake (since it doesn't really matter for illustrative purposes).
What is the difference between an invention and an implementation?
The difference is in the level of generality: an invention is a general solution to a general problem, whereas an implementation is a specific solution to a specific problem*.
So in the case of US 9083821, the specific problem is that users with hearing impairment may not fully enjoy some music when it plays on their device. The specific solution (and how they might intend to put it into practice) is to adapt a music app to vibrate the device in response to the music. Apple could have patented this. However, by limiting themselves to their particular implementation, they would end up with a very narrow protection which would not cover (perhaps a baby monitor for people with hearing difficulty) which uses the same technology but involves a very different implementation.
Thus the drafters would have considered what the general problem is, which is how to convey audio information to a user who cannot hear. The general solution (and the essence of their invention) is to receive an audio signal, convert part of it to haptic feedback, and present the feedback. This covers their specific implementation. But it also covers any other kind of implementation using the same invention. The result is a broad, powerful patent.
How is this reflected in US 9083821?
Primarily this can be seen by considering the scope of the claims. Claim 1 is:
1. A method performed by one or more processes executing on an electronic device, the method comprising:
receiving an audio signal comprising a range of audio frequencies including high frequencies and low frequencies;
converting a first portion of the range of audio frequencies into haptic data representable as haptic feedback comprising at least one of a vibration based on a stored vibration pattern, temperature variation, or electric stimulus to a human user;
shifting a second portion of the range of audio frequencies to a different range of audio frequencies, wherein the second portion corresponds to a range of audio frequencies that a user of the electronic device cannot hear, and the different range of audio frequencies corresponds to a range of audio frequencies that the user can hear; and
presenting the haptic data as haptic feedback so as to convey audible information.
There is very little in this claim related to its actual implementation. The only mention of hardware is in the preamble ("an electronic device"). Moreover, there is no mention that it would be included in a music listening app or that it helps hard-of-hearing people. Instead the claim purely relates to the invention, which is fundamentally just an algorithm.
Claims 15 and 29 do recite some general hardware, but still don't recite a particular implementation.
What about the description
The description is very closely tied to the claims. From reading through the description, you have no knowledge that this will be integrated into a setting for the iOS music app (I assume). While it would be permissible to include these details in the description, there is probably little advantage to doing so. If the general invention is known, the specific implementation will likely be obvious (so wouldn't be useful for amendments anyway). Alternatively, they may have just wanted to keep their competitors guessing.
What should a future drafter do?
Start with your specific problem and solution, which you will likely be familiar with (and which will hopefully be novel and non-obvious). Then consider what how you could your problem and your solution without losing the novelty/non-obviousness. For example, instead of vibrating a device, you might "present haptic feedback". Instead of converting high tones, you might "convert a first portion of the range of audio frequencies". And so on, until you're left with a broad conception of what your invention is.
* The terms "problem" and "solution" have a particular meaning in European patent practice, which I don't intend here. I am trying to use them in a more general sense.