"Matrix reports are similar to summary reports but allow you to group and summarize data by both rows and columns. They can be used as the source report for dashboard components. Use this type for comparing related totals, especially if you have large amounts of data to summarize and you need to compare values in several different fields, or you want to look at data by date and by product, person, or geography. Matrix reports without at least one row and one column grouping show as summary reports on the report run page."

Below is an example matrix report that is summarizing by date and by stage. 

Taken from: https://help.salesforce.com/articleView?id=reports_changing_format.htm&type=0 


"Joined reports let you create different views of data from multiple report types. In a joined report, data is organized in blocks. Each block acts like a “sub-report,” with its own fields, columns, sorting, and filtering. You can add a chart to a joined report. For example, in the following sample, the joined report pulls data from two report types related to the Positions object. Together, the report shows applications received from job ads posted for each position."

Below is a graphical explanation of joined reports.

Taken from: https://developer.salesforce.com/docs/atlas.en-us.fundamentals.meta/fundamentals/adg_reports_formats.htm