Inter- implies to me something between disciplines. It's the interactions and outcomes that come from 2 or more disciplines working on an idea together. I do make a distinction between multi-, the use of information from different disciplines in order to solve a predefined problem. Inter-, may have a challenge that does not have predefined questions and goals but uses the disciplines to better understand the challenge. Trans-, is on the farthest end, looking for themes that can be explored.

Curiosity-driven research stemming from, or leading to, the cross-pollination of influences and understandings held by established disciplines.

Interdisciplinary means you enter into the disciplines to realize the work

In "A Rough Guide to Interdisciplinarity" Jessica Graybill and her colleagues see interdisciplinarity as distinct from multidisciplinarity or other calibrations. Instead, interdisciplinarity is “the use of an innovative conceptual framework to synthesize and modify two or more disciplinary approaches to deal with a research problem.”

In "A Dictionary of Education" Derek Rowntree positions the interdisciplinary as when "two or more disciplines are brought together, preferably in such a way that the disciplines interact with one another and have some effect on one another’s perspectives.”

According to Prof. Veronica Boix Mansilla, in “Interdisciplinary Work at the Frontier," interdisciplinarity is the purposeful, disciplined, and integrative “pursuit of an advancement in understanding – i.e. an enhancement in our capacity to solve problems, produce explanations, create products, and raise questions – by means of bringing together bodies of knowledge and modes of thinking stemming from two or more disciplines.”