The term phoneme means one of the characteristic sounds of a given language. And phonetic text was just text written with symbols that corresponded to the phonemes. Then academia pushed things further. It was observed that, in some other languages than English, certain sounds that seemed the same to English speakers were perceived as different by foreign speakers and, conversely, some sounds that sounded different to English speakers were perceived as the same by foreign speakers. These different versions were dubbed “allophones” and phonetic text that did not take them into consideration was downgraded to “phonemic”.

The first case can be illustrated by Mandarin Chinese where tones differentiate phonemes.To the native speaker, the sounds seem quite different, to the non-native speaker they seem much the same.

The second case can be illustrated by Japanese. For example "lice" and "rice" are considered by English speakers to differ in the first phoneme, but for Japanese speakers the sounds are considered the same and indistinguishable, hence the old joke when seeing someone off at the airport "Have good fright".

The whole business has been terribly fogged. However, if you are only considering one language, such distinctions are pointless. I call S4 “phonetic” but an academic might classify it as “phonemic”, or maybe not.