The Background and Related Work chapters both provide detailed information obtained from other sources necessary to understand the rest of the report. However, there are some slight differences between the two:
Background: Technologies relevant to your MQP that you want to provide details on so a reader will understand your approach/methodology.
Important: The reader should be told how the background technologies are relevant to your work, how you use them in your solution, or methodology approach. This can be brief, but needs to be explicitly called out.
Related Work: Novel approaches others have tried to address your problem (i.e., research) that you want to discuss to present the "state of the art" and/ for comparative purposes with you work.
Important: The reader should be told how the work is related to your work. Is your approach similar/different to them? How? This can be brief, but needs to be explicitly called out.
The Background and Related Work can be two separate chapters or can be combined into one chapter, depending upon the size, scope and content.
These chapters are typically second in a report, right after the Introduction.
One of the key components of a good Background/Related Work chapter is organization. The layout and structure of the chapter is a contribution of your report. It represents a unique view of other work/technology from your vantage point.
A good approach to tackling the related work is to:
Gather resources (blogs and websites and especially peer-reviewed papers). Cast a wide net initially, but then narrow down as you get a better sense of relevancy. Read appropriate work in detail and summarize with notes.
Organize into groups based on similarities. These groups likely become sub-sections in your chapter. Place them in an outline.
Provide a summary of the works in the outline. Typically: what is the approach, what were the methods, what did they find. Make sure to explicitly state the relevance of the work to your project. This doesn't have to be done for each paper but can be at the end of a subsection.
Figures taken from your cited sources are allowed (and often make the chapter much better), but should also be cited in the figure caption.
Since nearly all the information in Background and Related Work is external, it needs to be cited, accompanied by an entry in the References section of the report.