These terms were devised in the late 20th century analysis of Classical Japanese, originally, for the difference between -(さ)す (glossed as externally instigated) and -(ら)る (glossed as internally instigated). This exoactive vs endoactive reflects 18th century Japanese use of 他動詞 vs 自動詞 (tadoushi vs jidoushi).
In more traditional Western-orientated linguistic parlance, this is equivalent to transitive vs intransitive; in Modern Japanese, this is how it is presented to students. E.g. 散る (ちる) chiru vs 散らす (ちらす) chirasu. However, there are pairs even in Modern Japanese which definitely do not fit this description, e.g.
heya (w)o deru
to go out of / leave the room
... where there is an explicit object, but the verb is endoactive (with る), yet transitive. Contrast this with:
kekka (w)o dasu
to yield / come out with results
... where there is an explicit object, the verb is still transitive, but exoactive (with す). There is also a school that calls them causative vs inchoative pairs.
However, on application to Chinese, endoactive vs exoactive was used for directional transitive verbs, e.g.:
"buy" 買 mǎi vs "sell" 賣 mài
"buy grain" 糴 dí vs "sell grain" 糶 tì
"hear/smell" 聞 wén vs "ask" 問 wèn
... and a wide range of pairs that fit a similar semantic alternation. This regular(ish) association of exoactive = Middle Chinese 去聲 (departing tone) implies some sort of regular morphology in Old Chinese, which is believed to be a final *-s suffix, which later (in the Han?) became *-h and ended up in departing tone.
Schuessler expands on this endoactive/exoactive distinction with the endopassive/exopassive one, as well as providing a simplex (neither -active nor -passive) version, and associates them with different proposed derivational phonology by their outcomes in Middle Chinese. Some of the above examples were reallocated.
This tonal difference is what accounts for 取 vs 娶, which in Middle Chinese have rising and departing tones. This distinction is preserved in (colloquial) Min but lost in Mandarin and (most of) Cantonese. However, if "take" is the endoactive (internally motivated) direction, then how is "to take as a wife" an exoactive (externally motivated) one? That's the semantic leap that Schuessler has to make, and provides an explanation for:
However, the key was apparently the person as indir. object.