Why should a student with a BS be admitted rather than a student with a MS?

Students who have a BS can apply for PhD programs like students with a Master's degree (in the US). I was thinking why should students with only Bachelor degrees be admitted while many with Masters degree apply too. I thought the program may differ for these two admitted students. So, my question is basically this:

Is there any difference between the PhD program that an admitted student with a BS starts, and the PhD program that a student with a Master's degree goes through? (assuming they are admitted to the same program at the same university)