Learn English – ny difference between “an epaulet” and “shoulder board” when speaking about military uniform

Generally, famous refers to recognition, and popular refers to reputation (of a person) or frequency (many people use a thing or visit a place).

Famous often, but not necessarily, has positive connotations. Knowledge of the famous person, thing or event is widespread.

Popular usually has positive connotations, or when referring to a place, it means it is visited by many people. The person, place or thing is largely well regarded among the people who know of it, but doesn't necessarily mean a lot of people know of it.

Perhaps it's easier understood with an example.

• A famous restaurant: Is well known. The name of the restaurant is recognized, perhaps because a well-known chef founded it, or it advertises a lot, or a well-known event occurred on the premises.
• A popular restaurant: It's usually busy. The majority of people enjoy eating there. Or maybe they don't, but they go there because the food is cheap, or it's the "place to be." Outside of the people that eat there, it may or may not be well known.

A restaurant can be both famous and popular (everyone knows about the restaurant, and many of them go there), or popular but not famous (only the people that frequent the restaurant know of it), or famous but not popular (making it infamous).

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.