You fired 3 questions back to back.
1. Recruitment, indeed, is a very integral part of the HR avenue. The foremost insight of the goals set for an HR team is to manage the HUMAN RESOURCES and closing positions with the best suited candidate makes all the efforts worth put. There are quite a number of modes by which a Recruitment Executive administers this, one of the most hot pick these days being US Staffing. So, yes, US Staffing is included in Recruitment and thereof in HR exercises.
Now will US Staffing get you to land a lucrative job abroad? The probability is very slim as the job is entirely outsourced. You definitely get foreign trips once you start to show your mettle in the field but that is neatly for a short time and only because the firm wants you to get a taste of profiles and attributes of the profiles you would be hiring next (this comes from my personal experience in the arena).
2. HR Recruiter is made to recruit for all the positions that are open in an organisation. These positions may/may not be solely of IT staffs. While IT Recruitment, as the name speaks for itself, is promptly concerned with IT Recruitment. You don't get to lay your hands on Non-IT staffing.
Having said that, the terms HR Recruiter and IT Recruiter have been used quite liberally for quite sometime.
3. HR and Admin are two completely different arenas. HR is the middleman between the employees and the employer which promises the employees' well being. Admin, on the other hand, seeks to provide resources for the well being of the whole workplace. HR is a part of admin and the KRA's are strictly different for the two. However, these two streams can also be used interchangeably depending on the administrative convenience of the firm. Roughly putting, Admin is the Management's tool to keep the firm functioning as it must while the HR strives to make the best use of the personnel involved in tasks.
Hope I made any sense here.