Is it plagiarism to copy the form and structure of an article?
You've done nothing wrong; most manuscripts follow the same structure.
Consider the following recommendations for structure: (1) Introduction, (2) Materials and Methods, (3) Results, and (4) Discussion. Would it be wrong to adopt that structure? No. It's a very common style and is widely adopted.
The OP added:
It's not just the [structure] that I followed, but the language - i.e. transition words.
Transition words, e.g., https://msu.edu/~jdowell/135/transw.html, are standard, so they shouldn't create an issue.
The order of the introduction is the same, for example.
That's just a different form of structural issue, hence, this isn't a problem.
I said why the world needs the paper in a similar language even though there was two totally different topics and subject matters.
Such a style is advocated by many, e.g., Simon Peyton Jones, so that shouldn't create an issue.
Note: Without seeing the texts, we cannot comment on specific issues.
Academic writing is fairly standardized. Most disciplines follow a standard template, usually a variety of the following:
- Introduction
- Why the world needs this paper
- What the literature already says on the topic and what this paper contributes
- How this paper is organized
- Background: An elaboration in roughly five paragraphs on the first paragraph of the introduction, setting the stage for the analysis and making the reader aware of the context needed to understand the paper
- Theory: An inventory and perhaps formalization of the theoretical concept(s) or model(s) used in the subsequent analysis in roughly five paragraphs
- Methods
- How the theory was operationalized
- How the data was generated
- How the data was analyzed
- Analysis: Two or three subsections, each making one major claim that relates to the overall research question. Explains how the data/observations inform the theory and/or vice versa.
- Conclusion
- Restatement of the main thesis and argument in theoretical terms
- Discussion of the contribution to the literature
- Implications for future research
If you used a format similar to this one, you didn't plagiarize; you just followed academic writing convention, which is good. And so did the paper that you used as a template.
This is something that has come up in comments, but not yet in answers: you should not have written that paper that way. You copied parts of the other professor's wording (perhaps at long stretches) and plugged in your own material. The content and the quality of writing (e.g. persuasive style, apt wording) are both important in academia. In fields like philosophy or literature, both may be equally important, whereas in experimental sciences many authors and readers would be happier if articles just consisted of figures, tables, citations, and bullet points. In all fields, though, there are people who put extra effort into writing well and would be particularly annoyed at having their structure and unique wording copied.
This is in the realm of plagiarism, but it does not make the top 28 guidelines for avoiding plagiarism offered by the U.S. Department of Health and Human Services' Office of Research Integrity. Because you appropriated the peripheral wording and not the content, this is more of a gray area (depending on exactly how much was borrowed), and it does not impact whether the scientific record should be corrected: your results still stand, and your ideas are still yours. This is one of the reasons no one so far seems to be in favor of retraction.
I've even heard writing advice that you SHOULD copy the argumentation structure of other papers, but usually there are caveats about not taking everything from the same place. In creative writing classes, there are often assignments to write in the style of some other author, as practice, but the goal is to help the writer pick up different tools of expression, and in the final work for public consumption it shouldn't be obvious that the writer was mimicking someone else.
This issue probably still feels unresolved. The first time I misjudged a traffic light and essentially ran a red light, I was shaken and pulled over and expected the police to immediately find me and ticket me. But I realized that mistakes happen, and sometimes the correct way to rectify them is not to seek out appropriate punishment for yourself but to be vigilant about not making the same mistake again.
You did a good thing by reaching out to the original author, and because they do not want a retraction, you can consider this matter resolved. (You may want to save a copy of that correspondence, on the exceedingly remote chance that someone raises this as an issue later, after discovering it through a natural language processing exercise or something. Plus, if this article ends up in your "Collected Works" someday, as GEdgar suggested in a comment, you can then quote that author's kind correspondence in your commentary.)