One similarity between persuasive speeches and persuasive essays is that they both are "persuasive," which means that they both attempt to convince people of a certain position.
The first difference between the two is that speeches need to focus on the way the words sound while read aloud, and they usually require a particular intonation in order to be effective. Essays, as they are not always read aloud, do not need to focus on this as much.
The second difference is that speeches tend to be shorter and more emotional. This is because the speaker is addressing a large audience with a variety of attention spans. Essays, on the other hand, can be longer and more detailed.
