What are the differences between fragment and run ons sentence?

Answer

There are several types of faults when it comes to grammar. In fact, most people make these mistakes at least once every day. Some errors include fragments, run-ons, spelling errors, punctuation errors, and capitalization errors.
Fragments are essentially incomplete thoughts. These happen when a writer fails to, for lack of a better word, complete a sentence. Take a look at the examples I've provided you:
Complete: There are many different species of fish, such as tuna, salmon, and trout.
Fragment: There are many different species of fish. Such as tuna, salmon, and trout.
Run-on sentences express a complete thought, but are often the combination of two or more sentences. Other times, they are sentences that do no contain commas or other punctuation.
Correct: Jimmy went to the market with his mom. While at the market, Jimmy and his mom purchased some eggs, sausages, and hashed browns.
Run-On: Jimmy went to the market with his mom while at the market Jimmy and his mom purchased some eggs sausages and hashed browns.
Read this out loud. You'll notice that this is actually a mouthful to say without proper punctuation.
Spelling errors are a very common mistake that are encountered in sentences. These errors are made either because we don't take time the time to be careful with our spelling or simply because we don't know the correct way to spell a word. Below is an example of some of the most commonly misspelled words:

• There: This word applies to a designated location.
• Their: This word applies to the ownership of something to multiple individuals.
• They're: This word applies to the state of being of multiple individuals.

Examples:
There is a city called Los Angeles. Meaning that there is a city called LA.
Their city is called Los Angeles. Meaning that the peoples' city is LA.
They're in a city called Los Angeles. Meaning that people are in LA.
Punctuation is also a very common error made within sentences. But how do we know when to use the right punctuation? Sometimes, this can be a little tricky. Let's talk about commas. These are use to break down a sentence and create small pauses. Here is an example of using a comma.
Correct: If you don't like this food, you can always try that food.
Incorrect: If you don't like food you can always try, that food.
Notice how the comma breaks the flow of the sentence.
Capitalization is another commonly made mistake that people make, especially with today's internet slang. There are two reasons to capitalize letters. Words at the beginning of a sentence or quote should always be capitalized. In addition, the name of a person, proper place, or business should always be capitalized. For example:
Correct: This spring, John will be applying to attend California State University, at Fullerton.
Incorrect: this Spring, john will be appling to attend California state university, at fullerton.
Notice how the wrong word was capitalized.
So, let's see all of them put together:
Correct: This spring, John will be applying to attend California State University, at Fullerton. Cal State Fullerton is down the street from Fullerton College, which is the city's community college. There are many students who attend classes at Cal State Fullerton, with their hopes and dreams waiting to be fulfilled. They're all in the process of becoming something greater than they already are.
Incorrect: this Spring, john will be applying to attend California state university at fullerton. cal state fullerton is down the street from fullerton college which is the City's community college there are many students who attend classes at cal state fullerton with there hopes and dreams waiting to be fulfilled. Their all in the process of becomming something, greater than they already are.
Notice how the words "this" and "cal" are at the beginning of the sentences? Take a look at that run-on sentence. There should be a period in between "college" and "there". And with that said, "there" should be capitalized.
Now do you see that they aren't capitalized, when they should be? John, Cal State Fullerton, California State University, and Fullerton College should all be capitalized because they are names of a person and proper locations. Their is the only word that was capitalized when it should be, but it is spelled wrong. There is only one comma, and it's in the wrong place.
I do hope that this little session helps you. Feel free to play around with English. :-)