This is a very difficult question to answer as there are many people who would answer it in different ways. We can see from the three links below that people who see themselves as authorities on the subject can produce statements that directly contradict each other. For example, one of the links below says that all fundamentalists are evangelicals while not all evangelicals are fundamentalists. At the same time, a different link says that “Fundamentalists are not Evangelicals and Evangelicals are not fundamentalists.” I would strongly suggest that you consult the text or the notes from your class to see what distinction your own instructor expects you to make between these two movements.
My own view is that fundamentalists are a subset of evangelicals. All evangelicals hold to a set of what we would think of as traditionalist beliefs about Christianity. For example, they all believe that the Bible is the inerrant word of God and that the only way to salvation is through Jesus Christ. However, we can also say that fundamentalists are much stricter than other evangelicals and that they, in the words of one of the links, “tend towards intolerance.”
For example, fundamentalists tend to be much less accepting of other people who do not share their specific beliefs. This is even true of their thinking about other people who call themselves Christian. In other words, fundamentalists will tend to believe that other groups that call themselves Christian are seriously misguided. Fundamentalists will refuse to enter into communion with these groups. They can be willing to split over such seemingly minor issues as whether the King James Version is the only true version of Scripture.
Fundamentalists are also more dedicated to the idea that the Bible is to be read literally in all instances. Evangelicals do believe that the Bible is inerrant, but they do not believe that it is all to be taken literally. Instead, they are willing to accept the idea that parts of the Bible are meant to be taken metaphorically.
In short, fundamentalists are stricter about their beliefs and less willing to accept any deviation from those beliefs than evangelicals as a whole are. Please read the links below for more specific differences between the two.