Depending on your purposes, both phones and phonemes can be described using articulatory, acoustic, or additional features. When you propose that a sound has a psychological status, you are proposing that it is a
phoneme; when you just want to refer to a sound in a way that is understood by people with phonetic training, it is a
phone.
One way to understand this is to consider experiments that look for
categorical perception. A classic experiment takes an audio recording of somebody pronouncing an unaspirated alveolar voiced stop (i.e. "d"), and modifies it by inserting silence between the stop burst and the onset of voicing. By adding more silence, we can create a continuum of stimuli with different amounts of time before voicing. The amount of time before voicing is called "VOT." Now, when I am talking to you and describing these stimuli, I just want a convenient language for describing acoustic or articulatory processes with experts, and so I'm talking about phones. That is, I'm only interested in giving you a concise summary of what these sounds are, I'm not attributing them any special status in the language or speakers' minds. How I describe them, what you wanted between the brackets, will be determined by the kind of information I want to convey to you. In this case, it's a feature specification, plus some detail about a manipulation to the waveform.
Now let's talk about what we might use these stimuli for. In one experiment, I could have non-linguists listen to random pairs of these stimuli, and say whether the two recordings they heard were "the same" or were "different." If you do this with English speakers, you will find that speakers tend to say that they are "different" if one stimulus has a VOT less than ~40ms and the other has a VOT more than ~40ms, but will tend to say that they are "the same" if both stimuli have VOT greater than ~40ms or both stimuli have greater stimuli less than ~40ms, even if the magnitude of the difference in VOT is the same. That is, they will tend to say "the same" for stimuli with VOT of 50ms and 70ms, but "different" for stimuli with VOT of 30ms and 50ms, even though both stimuli pairs have the same difference in VOT (20ms), because the first pair does not cross the 40ms boundary while the second pair does. For another experiment, you might play two stimuli, then play one of the two stimuli again and ask if it was similar to the first or second recording they heard. If the two initial recordings cross the 40ms boundary (i.e. one has VOT above and the other has VOT below), then English speakers will accurately classify the third recording. If the two initial recordings do not cross the 40ms boundary, then English speakers will not accurately classify the third recording.
With these results, we might propose that there is a perceptual category for alveolar stops with VOT above 40ms, and a different perceptual category for alveolar stops with VOT below 40ms (I have just described
Liberman et al (1957)). With this proposal, we are not just trying to describe language data, we are attributing some kind of entity either to the language or to speakers' knowledge about the language. A phoneme is this second kind of entity. It is not simply a convenient way to summarize language data to an expert, it is the attribution of a theoretical entity either to a language or to speakers. How we describe the perceptual category will be determined by the kind of entity that we want to attribute to the language or speaker. For example, follow-up experiments showed that the 40ms boundary can be pushed around by
context, so maybe we need the description of the entities to include context. Alternatively, perhaps we like the theoretical cleanliness of certain frameworks, like Optimality Theory, that commit to describing phonemes in particular ways.
Does that make sense? The description of phones and phonemes may vary widely depending on the kind of information you want to encode, but phones are for communicating with expert linguists (or engineering speech technologies) while phonemes are theoretical entities.
