Are there any differences between Master's admissions and Ph.D admissions in the US?
The difference is huge, at least in my field, computer science.  Master's programs are typically money-makers, with students paying full tuition.  Some programs are purely coursework; others require Master's theses or projects.

In contrast, PhD programs accept many fewer students, none of whom pay tuition, instead receiving stipends paid for by fellowships, teaching assistantships, and research assistantships.

Because of the difference in the size of these programs and who pays whom, PhD programs are far more selective.