Run-on sentences and comma splices are errors made by incorrectly joining sentences.
We went home and we cooked dinner. run-on
Michael Jordan retired, then he came back. comma splice
He helped the Bulls, maybe he can help the Wizards. comma splice
Notice that each of these sentences is made up of two smaller complete sentences.
We went home we cooked dinner
Michael Jordan retired then he came back
He helped the Bulls maybe he can help the Wizards
When you join small sentences to make larger (compound) sentences, there are two ways to use punctuation correctly.
use a semicolon where the period separating the sentences would go
use a comma and a FAN BOYS word (for, and, nor, but, or, yet, so)
Of course, you can also leave the sentences separate.
We went home, and we cooked dinner.
Michael Jordan retired; then he came back.
He helped the Bulls. Maybe he can help the Wizards.
Common mistakes to watch out for
The only time you will be able to use a semicolon or a period is when a complete sentence ends. If you use a word besides a FAN BOYS word to join the sentences, you will probably need a comma. Those other words, like because, if, whenever, start a dependent clause: that means they can’t stand alone, so you will never use a semicolon to join them.
Because he missed the game, Michael Jordan came out of retirement.
We have a party to say good-bye whenever someone retires.
If Michael returns to baseball, we can all go see him play.
In each of these cases, the sentences are not made up of two smaller complete sentences. They are made up of one complete sentence (independent clause) and one piece of a sentence (dependent clause). Since we need more information to make the dependent clause make sense by itself, you will never punctuate it with a period or a semicolon.