What does Graduate school mean: Master, PhD, or both?
Graduate school refer to a school that offers advanced degrees (MS, PhD, or both), even if a school offers only MS degree, it is still called graduate school. I think med-schools are also called graduate schools (since they offer MD and OD degrees).

There will always be some sort of an admission process. Student usually apply for MS program, finish it then join a PhD program. Although in some cases, students can combine MS and PhD together and save 1-2 semesters.