They are the same letters except few ones 

but there's in arabic something which called "shakel = الشكل" 

it means some marks which guide you to how to say / pronounce this letter/word

there's alot of these marks to guide you better 

________

"if you do mistake in this marks maybe the meaning of the word change"

______

sorry for my english here is too bad :D

hope I can explain to you well, the form which is found in holy Quran is the fluent form, the marks over the letters related to the grammar and also the pronunciation.

so the tow forms are wright , but it depends on the satiuation, if you need to just write in chat that is enough to write without the marks over the letter, but when you write Holy Quran, it is prefered to use this marks as you can.

well as Mai said !! 

But i think we spell them the same in Quran and when we  talk with people :) 

Salam 3alikom bro ! The letters in Quran Karem are written as of Modern Standard Arabic . It has a special spelling and writting . 

OK. Thanks to you all, but I did know how to read the original Arabic. Because I used to read Arabic that had the mark. 

Does the language in the Quran same with the language that you use everyday ?