The above question is self explanatory, still I would like to break it into two parts.
Q1. What is the difference between abstract and summary/conclusion?
Q2. What is the difference between summary and conclusion ?
The abstract is written for the potentially interested reader. While writing it, keep in mind that most readers read the abstract before they read the paper (sounds obvious, but many abstracts read like the authors did not consider this). The abstract should give an impression of what the paper will be about. Do not use jargon or any abbreviations here. It should be understandable for non-specialists and even for people from fields somehow far away.
The conclusion should conclude the paper and is written for the reader who already has read the paper. In other words: most readers have read the paper when they read the conclusion. Again, this sounds obvious but, again, a lot of conclusions do not read like this. It does not make sense to write a conclusion like "we have shown this and that by using this and that method". Well, this is what the reader has just read (and what he may know since he has read the abstract). A proper conclusion should tell the reader what she can or he could do with the newly acquired knowledge. Answer the question "So what?".
A summary sums up the paper. I am not sure if a paper needs a summary.
I've written some tips for abstracts some time ago:
A1: In the context of a journal article, thesis etc., the abstract should provide a brief summary of each of the main parts of the article: Introduction, Methods, Results and Discussion. In the words of Houghton (1975), "An abstract can be defined as a summary of the information in a document". The Conclusions (in some cases also called a Summary) chapter is a summary of the main ideas that come out from the discussion (e.g., Katz, 2009) and hence only a subset of the abstract. Usually, the Conclusions sum up the discussion whereas the abstract only reiterates the most important of the conclusions.
A2: The difference between a summary and the conclusions is less clear. First, it is not clear if the summary is to be compared with the Abstract or the Conclusions. A summary may also be more appropriate as Conclusions when writing an overview where the conclusions may not be easy to identify. As stated above some journals use the word Summary instead of Conclusions. Sometimes this can also be labelled Synthesis and cap off a lengthy discussion.
Houghton, B., 1975. Scientific periodicals: their historical development, characteristics and control. Hamden CT, Shoe String Press.
Katz, M.J., 2009. From research to manuscript. A guide to scientific writing. Second edition. Berlin, Springer.
A conclusion section might for example include speculations about some patterns in the data, or proposals for future research. It basically is really the only place to put your opinions. A summary I expect would not include any opinions and just re-iterate the findings and weaknesses in the study.
As the other answer mentioned, the abstract should include all the main aspects of the paper in an abbreviated form - the topic, the hypotheses, the participants and study design, and the results.
Abstract: Author short story about what is in it (no matter good or bad, valuable or scrap) Conclusion: Authors statement about the findings justified by the detailed content (findings/achievement/affirmation of a doubtful fact/negation of an established belief...etc) for a reader who has a guided-travel across by the author.