It depends on the context. "Can" implies basic ability, and "know how" implies a learned skill. If a person has not learned how to write, then the person "doesn't know how to" write, and the person also "can't" write. If a person does know how to write, though, they still might not be ABLE to write, for various reasons. For example, if a person has a broken arm, you can ask, "Can you write?" The person will understand that you're asking whether they can write with a broken arm. You're not asking whether the person has learned the skill of writing. However, you could also ask a four-year-old child, "Can you write?" In this case, most people would assume that you're asking whether or not the child has learned how to write letters and words. The meaning is the same as "Do you know how to write?" (Edit: looks like Jerry got to this one before me. :)

It depends on the context of the sentence. They can have the exact same meaning, or they can be different. Look at these examples. All of these have the same meaning. Do you know how to write? Do you know how to write Poetry? Can you write? In the above examples we are asking two things. 1. Can the person actually write? 2. Can the person write poetry? "Do you know how to write" or "Can you write" implies asking if a person knows how to write at all? Like a 4 year old. "Can you write"? but, by adding to the sentence we can assume that yes a person can write, but can they write in cursive? Can you write Java programing? Can you write a letter for me? Do you know how to write in Arabic? Do you see how the structure of the sentence can change the meaning(s)? Hope this helps, Jerry (Teacher/Tutor)

It's also fairly common to use the "can" construction to describe a high level of functioning, not a basic one. That girl can sing. (said watching someone sing exceptionally well on a reality TV show) A:There's a new kid trying out for the team. B: Can he play? (Is he a really good player?)

I think isnt the same the first one you can use it to ask some one who dose not know the methods of the writting and the second yu can use it to ask someone to write about thing that he knew it or not but he know the methods of the writting that is my opinion