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I'm really trying to understand the difference between the abstract and the introduction in academic writing.
In my opinion, the abstract just talks about the aim of the article and the structure of the article. And the introduction discusses the background of the topic and the central sentence of the whole article.
Is this a correct understanding?
The fields in which I've written papers (Computer Science, Psychology and Theater Science) the abstract is a compressed version of the whole article. Think one or at most two sentences each of introduction, method, result, and discussion.
The abstract exists as a kind of sample of the paper and should summarize the main/most important points in each of the above sections. Its goal is to give a reader a quick introduction into the article and in at most one page, preferrable even less, give them an idea of if they should read it or not. Most of your readers will be other students/researchers with a specific field of research or even an article of their own to write.
The introduction ... introduces the context and previous research pertaining to the topic of the article.
If you think of your article as an hourglass where the introduction gives a broader view of the topic and then the method and result focuses that broad view on the exact subject you've chosen, and then the discussion goes wide again, discussing implications of your results, connecting them to a broader context, etc.
This is how I was taught to write papers, however, this differs widely. Mostly, I think, because fields and the people in them are different, and many different levels of article quality are allowed to pass through.
For instance, psychology is extremely scientific. I can't recall a single paper that didn't follow the same format and they all had a very high quality. Especially papers on experiments. Probably because experiments fit perfectly into the intro-method-result-discussion format. (And psychology is all about the experiments!)
Computer science on the other hand sometimes felt like coder high-school, at least when you compared to psychology.
Theater science... Oh my... I wrote a first-year paper, and only in critique (is that what it's called when other students critique it?) I finally understood that I'd actually not fully understood what I was doing... (And yes, I was sober the whole time!)
The abstract is a brief summary of the whole work, including the conclusions. A reader should be able to read the abstract and know the key points of the work that they're reading. Occasionally, an abstract may be brief to the point of humorous, e.g., an article with the title “Is the moon made of green cheese? A spectrographic analysis” might have an abstract whose entire contents are: “No.”¹ More often, it will be a complete précis of the work boiled down to a paragraph or two.
The introduction is there to bring the reader into the work. Differing writers may take different approaches. For some, they may organize their writing in the “Tell the reader what you're going to say—say your thing—tell the reader what you said” style, in which case the introduction might seem very similar to the abstract in its function. Others, will take the opportunity to motivate what they're writing about. Why is the problem attacked in the work worth attacking? What were the challenges in attacking it? etc. Some writers may eschew an introduction entirely and just dive into the main question of the work. It's a matter of style more than anything else.
The purpose of an abstract is to help researchers understand if the paper in question is useful to them. An introduction's purpose is to help the reader better understand the paper they are reading.
It probably goes without saying, but there are a lot of research papers out there. Finding the information you want can be like searching for a needle in a haystack. Researchers don't have time to read all the papers that aren't relevant to their work, so instead once they have found a collection of likely papers they read through the abstracts in order to further narrow down the list.
As such, an abstract needs to stand on its own as representative of the paper. Your goal is to make as clear as possible what information the paper contains, as concisely as possible.
An introduction, on the other hand, is part of the paper. Someone reading the introduction has already decided to read the paper. The introduction's purpose is to frame what will follow so that the reader can best understand it.
