a run-on
A run-on sentence is a sentence that has two or more complete thoughts without proper punctuation. This makes the sentence grammatically incorrect. For example: I have a dog she runs fast. There are two complete ideas, but they aren't punctuated correctly. It's also missing a conjunction. Two join the ideas, it must be changed to: I have a dog, and she runs fast.
A fragment is an incomplete sentence. Most fragments are dependent clauses. For example: Since the dog runs fast. This is a fragment because of the word "since". Since tells you that there should be some follow up information about the dog running fast. Since the dog runs fast, she must always be on a leash.