While position and post can often be used interchangeably in reference to employment or occupation, I believe
- Post more strongly connotes an assigned station, especially a specific geographic place and often for a temporary or rotating assignment.
- Position on the other hand more strongly connotes a rank or class.
In my experience, if you ask an executive for her post, she may say "the Lisbon office," whereas if you ask for her "position," she's more likely to say "Vice President for Ibero-European Operations" or some such.
Both position and post can trace their roots back to the Latin verb pono, ponere, meaning to put or to situate something, but the latter, according to Merriam-Webster, came via Middle French and Old Italian having acquired the meaning of a relay station along the way. This sense of post is of course carried through in its courier-related meanings, i.e. we send mail through the post (NAmE) or send a post through the mail (BrE).
The U.S. Army refers generically to its installations as "posts," and a soldier is "posted" to a particular assignment as well as given a particular "post" when on duty. In the same way we can speak of journalists or diplomats being sent to a "post" like the Tehran bureau or the Shanghai consulate or of waitresses or warehouse workers being sent to a "post" like tables 20-24 or delivery dock C. In both cases, we are speaking of a temporary assignment to a particular station.
So in your example, I would think either of
[He] applied for the position of head of human resources at [a big company].
[He] applied for the post of head of human resources at [a big company].
to be fine, the former preferred if "head of human resources" is a permanent role, the latter if it's a waystation for those on their way up or down the corporate ladder.