Summarizing x Synthesizing: Qual é a diferença?

Summarizing x Synthesizing: Qual é a diferença?
Em uma questão de um curso de inglês online, perguntava qual das seguintes palavras se associava melhor a algumas frases:

Summarizing, synthesizing, paraphrasing e citing.

Por exemplo, uma das frases era ""According to the paragraph from the textbook, A should sometimes be considered a Y; however, the professor indicates that A should always be classified as an X".

Bem, não entendi bem a diferença entre as respostas, principalmente as diferenças entre summarizing e synthesizing.

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Summarizing: Summarizing means stating a source's main ideas or points in your own words. A summary does not include the source's supporting details or evidence and is therefore shorter and more concise than its source. A good summary will give the reader a general sense of what the original material is without his or her having to read it.

Paraphrasing: Paraphrasing also means rewriting something in our own words. However, unlike a summary, a paraphrase is usually roughly the same length as the original.

Synthesizing: Synthesizing means integrating quoted, summarized, and/or paraphrased source material with your own ideas to create something new. You not only string together source material, you also explain, discuss, criticize, and interpret it.

Your example:

According to the paragraph from the textbook, A should sometimes be considered a Y; however, the professor indicates that A should always be classified as an X.

The first part of the sentence is "summarizing"; but the person adds the professor's opinion and creates something new, so the correct answer is probably "synthesizing".
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Summary - A shortened version of a text that highlights its key points. It´s purpose is to give the reader a condensed account of the main ideas.
In a dissertation, it summarize it in the conclusion. That is, the conclusion gives a shortened version of what the text states (with the key points).

Synthesis - Grammarly speaking, is shortening a statement by usually making the combination of two sentences in one, using infinitives to weld them togheter or using conjunctions etc.
It tides up you text, without highlighting the key point again. ... tences.htm ... nces-2.htm ... mpound.htm

In a no-to so grammar context, it is an abridged version, a shortened presentation of an ideology or set of ideas of a time, of a given project, etc.
That is, it is simply, the central idea of something, the ideology of it, the thesis, the substance/theme/direction of the text/conversation etc.

Sans much context, I am led to believe that what your question was asking where
What the text synthesis. That is, "the essence" of what the paragraph meant. Not the re-saying it, point by point.