A sentence fragment is usually a dependent clause, which means that it cannot stand or exist on its own. A fragment has to be included into a larger sentence in order to make sense. In the examples above, these would be sentence fragments:
Where the sidewalk meets the road
John and his very happy younger sister
On the other hand, run-on sentences are two or more independent clauses found in one large sentence, but either without a conjunction, or without any transition word to connect them. In the examples above, these would be run-on sentences:
The curtains are worn out, they need to be replaced.
Let's go, we have other things to do today.
The swings at the park were replaced recently, we love to play there.
It would be better to use a semi colon instead of a comma here because then the sentences would be grammatically correct.
