What is the difference between an explanation and an interpretation? Can someone please clarify for me if there is a difference between an explanation and an interpretation in scientific discourse? 

Whenever I am writing up results, I am careful to distinguish observations (which I associate with results) and interpretations (which I associate with discussion), because results are describing your data, where discussion is interpreting the data (which I always thought of as coming up with explanations for the results). However, I got into a discussion today with another scientist about the meaning the word explanation when they asked me add explanations into the results section of our paper (I thought they should go into the discussion). 

I am particularly interested in the differences between these terms in the natural sciences (my area), but welcome comparison of the terminology between the fields of math, natural science, and social science in order to help clarify their definitions.

Concisely, here is how I view the terminology:

Observation ≡ Result

Interpretation ≡ Discussion ≡ Explanation

Is this misguided? And if so, can someone please clarify?
I think I understand what your colleague is suggesting, and I think an example might help, so let me try:

I grabbed a (roughly) random article from the most recent copy of Nature by Govero, et al.

A bolded "explanation" in the Results section:


  At day 7, we observed high levels of viral RNA in all male reproductive tract tissues (Extended Data Fig. 4a). At day 13, we observed ZIKV RNA in germ and Sertoli cells in Rag1−/− mice, and this was associated with a decrease in TRA98+ germ cells and Lin28a+ spermatogonia and breakdown of the BTB. However, interstitial Leydig cells remained in ZIKV-infected Rag1−/− mice even though the architecture of the seminiferous tubules was altered (Extended Data Fig. 4c–d). Thus, damage to the testis appears to be mediated both by ZIKV infection and adaptive immune responses.


Versus an "interpretation":


  Our experiments with mouse-adapted ZIKV-Dakar show that infection causes testicular and epididymal damage in mice that can progress to reductions in key sex hormones, destruction of germ and somatic cells in the testis, and loss of mature sperm and fertility. Sertoli cells may be a key target for ZIKV in the testis, resulting in cell dysfunction, detachment from the basement membrane and dissolution of the BTB. Infiltrating inflammatory cells may amplify destruction of the testicular architecture.


So, in some ways there is a bit of overlap, and I don't know if "explanation" vs. "interpretation" are the best words used to differentiate them. I'm also not holding up this article as some optimal way of presenting things: opinions will no doubt vary. My personal opinion is that some contextualization is necessary in the results of all but the most straightforward papers. I think "explanation" is especially needed when you are discussing the control experiments you did, and it's a matter of personal style the order in which you present this, either: "In order to make sure XXXX wasn't a problem, we did YYYY" or "When we tested YYYY, we found ZZZZ, therefore XXXX did not contribute to our previous finding MMMM."

Essentially, in the results section, they didn't only state what exactly they found (i.e., virus levels and counts of cells), but they also explained what those result means in the context of what they are studying. In the discussion, they go further, interpreting the results in the context of other discoveries in the field and future directions for study.