acsenray basically covered it, but I wanted to add:
When you have two or more independent clauses (think of these as ‘sentences’ that can stand alone) that you want to join together, you have to do one of two things: (1) Use a comma + conjunction. If you can remember the acronym FANBOYS you won’t have much trouble. For, and, nor, but, or, yet, so. (2) Use a semi-colon.
Failing to insert the comma in instance (1), even if you have the conjunction, results in a run-on sentence.
Failing to insert the conjunction in instance (1), but including the comma, results in a comma splice.
When using a semi-colon, there should be a relationship between the clauses (just as there should be a relationship between them when using a comma and a conjunction).
Here are two independent clauses: 1. “Jim Lovell was on board Apollo 8.” 2. “He commanded Apollo 13.”
I could leave them separate, but since we’re referring to the same person and the same space program, it makes sense to combine them.
Instance (1): “Jim Lovell was on board Apollo 8**, and** he commanded Apollo 13.” This use of “and” suggests that I’m simply giving you the information. Compare that to: “Jim Lovell was on board Apollo 8**, but** he commanded Apollo 13.” The use of “but” suggests that I’m emphasizing Lovell’s command of the second mission.
Instance (2): “Jim Lovell was on board Apollo 8**;** he commanded Apollo 13.”
Either way is acceptable from a grammatical perspective. Stylistically, you should mainly stick with Instance (1) because the semi-colon is more stilting. Excessive use is distracting, but that is a matter of style.
You’ll see, often, that Instance (1) confuses many people into thinking that anytime there is an “and” or “but” that there must be a comma. See: “I enjoy swimming, and fishing.” The first part is independent–“I enjoy swimming.” The second part, “fishing,” is not complete (it lacks a subject.)
Vis-a-vis the serial (or Oxford) comma, as noted it sometimes avoids confusion. This: “I enjoy sausage, bacon, eggs and coffee.” suggests that the sausage and bacon are separate elements that I enjoy by themselves, but the combination of ‘eggs and coffee’ is something I enjoy mixed together, which would be pretty gross.