Different subjects in complementizer clauses are expressed - at least for sentences with two third persons - by means of an obviative suffix versus its absence in the subordinate verb.
Roughly, if the subject of the complement clause is different from the subject of the main clause, a suffix -yi- is used (except when one is subject, and one object).
As the presence or absence of this suffix has no effect on the shape of the complementizer, one could say that the same complementizer is used in different constructions.
The verbs meaning 'think' and 'want' probably behave in the same way. In both cases probably a construction 'I think/want it that ....' and a construction 'I think/want him/her that ...' can be used, with an inanimate resp. animate transitive verb. No contrastive examples are found in our data.
Source: Laverdure and Allard 1983: 21
Source: Fleury 2007
Source: Laverdure and Allard 1983: 322
Source: Laverdure and Allard 1983: 147
Source: Laverdure and Allard 1983: 21