What are some things that make prokaryotes and eukaryotes different? What are examples of prokaryotes and eukaryotes?

Prokaryotes and eukaryotes separate life on Earth into two main divisions. The main difference between prokaryotes and eukaryotes that most textbooks emphasize is that prokaryotes lack a nucleus, while eukaryotes have a nucleus that encloses their DNA. When the terms are broken down, we see that karyote refers to a 'kernel' or 'nut' because when scientists first saw a nucleus in a cell they thought it looked like a small kernel. 'Pro' means 'before' so you can remember that prokaryotes do not have a nucleus because they were around before a nucleus had developed. This is true when looking at evolutionary history as well. 'Eu' means 'true' so remember that eukaryotes have a true nucleus. Also, YOU (as a human) are a EUkaryote, and your cells indeed have nuclei (except a few, mainly red blood cells). 

Some other differences include that the DNA in prokaryotes is circular, while DNA in eukaryotes is linear. As a result of this, DNA replication occurs differently as well. In prokaryotes, DNA replication begins in one spot (one origin of replication), while in eukaryotes it begins in multiple spots (multiple origins of replication).

Another difference is that prokaryotes have no membrane-bound organelles, while eukaryotes have many different membrane-bound organelles including the golgi apparatus, endoplasmic reticulum, mitochondria, chloroplasts (for plants), and lysosomes. They both have ribosomes because they both need to make proteins, but the ribosomes in eukaryotes are larger than those in prokaryotes. The overall size of the cells are very different as well. Eukaryotes are much larger than prokaryotes.

Prokaryotes divide by binary fission, while eukaryotes divide by mitosis, a more complex process. Also, eukaryotes have the ability to use meiosis to create gametes with genetic variation, while the only way the prokaryotes can introduce genetic variation is to swap DNA with another prokaryote through the process of conjugation.

There are more complex differences, but these are the main differences between prokaryotes and eukaryotes that most students would be expected to know. I hope this helps!