I believe phonologists often don't make a distinction between allophonic and non-allophonic variation in the realization of phonemes, but, when they do, it goes something like this: allophonic variation is discrete, driven by a distinction that can be captured as a simple rule, maps to a plausible (and usually independently attested) binary distinction in articulation (and usually in acoustics), and often maps closely to a distinction that is phonetic in other languages (especially ancestral, or at least related, ones).
Consider the difference between the two /k/ sounds in kill and skill:
- The range in English /k/ sounds looks like two distinct blobs, one centered around a paradigm aspirated /k/, the other around a paradigm unaspirated /k/.
- If you measure articulatory physiology instead of acoustics, you get much the same results.
- Many languages—including relatives like Hindi—distinguish /k/ and /kh/ sounds on the basis of a +aspirated feature, and in fact the sound cluster for English /k/ is pretty close to the union of the clusters for Hindi /k/ and /kh/.
- /k/ may even be the result of a historical merger between separate /k/ and /kh/ phonemes in an ancestral language.
- The variation can be described by simple rules, like aspirated when it's the first sound in the onset, unaspirated when it's internal to an onset cluster.
Now try the same thing with the /s/ sounds in sill and skill. You get one big amorphous blob, caused by multiple continuously-ranging articulatory differences, none of which match up well with a well-attested phonetic feature used in any language. You can sort of explain why skill is usually less hissy because the tongue moves toward a stop in the middle, but it's hard to make a well-principled phonological rule like "onset = +aspirated".
Of course nothing is ever that perfect. For example, aspiration isn't really binary; you can aspirate harder or softer, and continue aspirating further or less far into the stop, and so on. And the cluster of English /k/ sounds is similar to the union of Hindi /k/ and /kh/, but not identical to it. But I think that's the distinction you're looking for: /k/ in kill vs. skill is the paradigm example for allophones, while /s/ in sill vs. skill is arguably (but it probably depends on a specific definition/theory) not allophonic.
So, what do you call variation like the hissiness of the /s/, or like your examples? There are all kinds of variation that have different names, but I don't think there's a name that covers all of the various kinds that aren't allophonic. I think what you're looking for is something like "(various axes of) non-allophonic variation in phoneme realization", or "non-allophonic (phonetic/segmental) variability", etc.; there is no simpler term.