When to use humanitarian sciences and human sciences in contrast? According to my uni materials, humanitarian sciences should have something to do with scientific function style of texts.
The OED has no entry for humanitarian sciences, but it does have one for human science, meaning, those academic subjects in which people or their actions form the object of study, as contrasted with the natural sciences or physical sciences; the humanities, (in later use esp.) the social sciences.
1833 E. B. Pusey Remarks Prospective & Past Benefits Cathedral Instit. in C. Thirlwall Let. to Revd. Thomas Turton on Admission of Dissenters to Acad. Degrees 14 Whatever schooling of the affections, or expansion of the whole mind and spirit, may be required for the right cultivation of the human sciences, must be much more necessary, when the things hereafter to be handled are the things of God. 1846
Times 8 June 4/3 If Adam Smith is a prophet, if political economy is the first of human sciences, and its doctrines above all contradiction, then Sir James is undoubtedly a very enlightened man. 1893 Geogr. Jrnl. 2 355 And the divorce between human sciences—history, economy, politics, morals—and natural sciences has been accomplished entirely by ourselves, especially during our century. 1943 Lasswell & McDougal in Yale Law Jrnl. 52 214 The great contribution of modern specialists on the human sciences is less in the realm of general theory than in the perfecting of method by which ancient speculations can be confirmed, modified or rejected. 2001 C. Freeland But is it Art? vi. 174 Art theorists draw on philosophy, and also on the human sciences, such as anthropology, sociology, and psychology, especially perceptual psychology.
If, as the OED suggests, human sciences is synonymous with the humanities, it is worth quoting those senses 2a and 2b of humanities.
2a. In singular and plural. Literary learning or scholarship; secular letters as opposed to theology; esp. the study of ancient Latin and Greek language, literature, and intellectual culture (as grammar, rhetoric, history, and philosophy); classical scholarship. In later singular use, chiefly in Scottish universities: the study of Latin language and literature.
2b. In plural (usually with the). The branch of learning concerned with human culture; the academic subjects collectively comprising this branch of learning, as history, literature, ancient and modern languages, law, philosophy, art, and music. Hence also in singular: any one of these subjects. The humanities are typically distinguished from the social sciences in having a significant historical element, in the use of interpretation of texts and artefacts rather than experimental and quantitative methods, and in having an idiographic rather than nomothetic character. Cf. human science n. at human adj. and n. Special uses 2.
Referring to the last few words of 2b, it seems to be suggesting that human sciences should be distinguished from social sciences, the latter making more use of "experimental and quantitative methods".
A humanitarian science is one concerned with the promotion of human welfare. Since the 1930s, the word "humanitarian" has also been used to describe a crisis that causes widespread human suffering (i.e. "a humanitarian crisis"). A person concerned with humanitarian sciences is a philanthropist.
Human sciences are those that are concerned with the nature of people and the way in which they interact with one another and with themselves; i.e. psychology, sociology, etcetera.