Is there a difference between "interdisciplinary" and "multidisciplinary" research?
Both terms involve, as you say, relating to more than one discipline. In practice, I think most people don't really bother distinguishing between them. (I typically don't.) So one shouldn't read too much into any particular use. However, as always there are some that debate the definitions. Sometimes - especially when larger teams are involved - the two terms are treated not as synonyms, but as different positions on a spectrum. When a distinction is made, it is typically to say that interdisciplinary work more deeply integrates insights of multiple fields, whereas multidisciplinary doesn't require the same degree of integration. E.g. Choi and Pak states in a review that

Multidisciplinarity draws on knowledge from different disciplines but stays within their boundaries. Interdisciplinarity analyzes, synthesizes and harmonizes links between disciplines into a coordinated and coherent whole.

Similarly, OECD's 2010 report &quot;Measuring Innovation: A New Perspective&quot; used environmental science and nanoscience as examples of multidisciplinary and interdisciplinary research areas, respectively (link to relevant page):

Interdisciplinary research that
relies on shared knowledge is created when fields such as physics and chemistry interact. Nanoscience typifies this
phenomenon. In multidisciplinary research, various disciplines address scientific and social challenges independently
rather than in collaboration and thus share research goals. Environmental research is of this type.

The 2015 The Oxford Handbook of Multimethod and Mixed Methods Research Inquiry provides a lot more details and development of these ideas, in particular in Chapter 8.

Interdisciplinarians integrate the best elements of disciplinary insights in order to generate a more comprehensive (and often more nuanced) appreciation of the issue at hand. (This may come in the form of a new understanding, new product, or new meaning.) As we shall see later interdisciplinarians often stress &quot;integration&quot; as the defining element of interdisciplinarity.
[snip]
Multidisciplinarity involves the juxtaposition of insights from different disciplines. It thus eschews the integration that is so critical for interdisciplinarity and transdisciplinarity. Multidisciplinarians are also less likely to evaluate the insights on which they draw. Multidisciplinarity can still be useful in some situations, notably where the insights of different disciplines are not in conflict and can simply be added together.