It appears to me that execution unit refers to hardware, specifically a portion of the computer's brain that can work at the same time as other parts on a different task. It seems to allow simple multi-tasking, as implied by Wikipedia's article on the execution unit. The article explains that Superscalar Architecture involves multiple execution units fetching commands at the same time.
An execution unit is like a worker. He has a job and does it until he is finished. Then he asks his boss what to do next and works on that. When you have multiple workers, you get more work done faster. An execution unit does low level tasks like 1+1
.
Moving onto unit of execution, it appears this is more about how the software runs, as evidenced by this microsoft article. A unit of execution, such as a thread, manages high level tasks involving many small steps like conquerTheWorld()
.