• ты = you, singular, informal
• тебя = you, as in а у тебя
• So ты and тебя means you.  Since both of these words mean you, why are they spelled differently?

On a similar note:

• Вы = you, plural, formal
• вас = you, as in а у вас
• So Вы and вас means you.  Since both of these words mean you, why are they spelled differently?

The reason why we have different forms of ты or вы - is that because Russian has got cases. 
Dictionaries only show nouns and pronouns in their Nominative singular case. In the above examples тебя and вас are the Genitive case of ты and вы

I understand that part, but what is the difference between ты and тебя?

And also between Вы and вас?

The difference is purely grammatical. Please compare the following sentences:
Ты знаешь меня. (You know me.)
Я знаю тебя. ( I know you.)
Both ты and тебя are translated as "you", but they have different grammatical functions. In the first sentence ты  is the subject of the sentence. And subjects in Russian sentences are always in the Nominative case. 
In the second sentence тебя is an object, because the subject in this sentence is  я (I). Objects in Russian sentences are expressed by other cases, such as accusative, for example.
The English word "you" doesn't reflect these changes, however, other English pronouns do have different forms (e.g. I - me; he - him; she - her; they - them)