Do rewritten urls count as separate pages?

I'm currently doing website translation using PHP and a MySQL database. I was going to rewrite my urls so that it looks as if there's a subfolder for the spanish language. Example:

English: http://www.example.com/rewritten_url/ Spanish: http://www.example.com/spanish/rewritten_ul/

I already know how to do rewrite rules, specifying GET variables and all that stuff necessary for this to happen. My questions are about SEO. Using the two urls that I mentioned above, do these urls act as if they are 2 separate pages or will the Google bots recognize that it's one page but a different url? If it's 2 pages, should I then specify on my sitemap.xml file that I have these 2 pages? and lastly, even if I didn't do rewrite rules, and left the get variables on the urls, would they still count as 2 pages?

I don't know a whole lot about SEO other than what I learned in the SEO Basics video, so I was just curious as to my approach. On a side note, for good user experience, is it better to continue using PHP and the database for translation, or should I consider AJAX to retrieve a translation and place it on the page. I ask these questions here on these forums since I already tried googling around for answers but I keep getting Google Translate API in the search results and that's not what I'm looking for.