Keywords and "Match Words" are used interchangeably. They both refer to the variations that google makes bold in the search results for your search term. When a factor name says "Keywords" it means any combination of these variations. When a factor says "Search Terms" it means exactly the search terms used to create the report.
About the Letter Grades
The letter grades were put in so you would have a way to show a client that there is always room for improvement. They don't actually mean very much in terms of SEO because websites rank relative to the competition. You can rank #1 with a C average if that is better than the competition. This is fairly common and it is rare for websites to have top grades.
Sentiment
These are the factors related to the use of sentiment words on the page.
Keyword Frequency
These are the factors related to keyword frequency of use on the page.
Trust
These are the factors that may be considered trust signals on the page.
Forms
These are the factors related to keywords used in forms on the page.
Ratings & Reviews
These are the factors related to ratings and reviews on the page.
Open Graph
These are the factors related to Open Graph tags on the page.
Authorship
These are the factors related to authorship markup or tags on the page.
Social Integration
These are the factors related to social integration. share and like buttons. Not to be confused with social signals which is how many likes and shares a page has.
Google Presentation
These are the factors related to how the page appears in the Google search results.
Links on Page
These are the factors related to the links found on the page.
Fringe
These are the factors that are weird and are generally associated with people trying to keyword stuff in unuasual places.
Misc
These are the factors that didn't fall into the other buckets.