Face is more related to honour, but its very hard to define.
I think giving a gift to prove to someone that your rich is not giving face (that would be if the gift is freely given without the intent of proving your wealth), but rather taking face or in western terms, showing disrespect.
I'd guess it might depend on whether you are in fact rich or not, and whether the gift is above or below the means of the gifted.
Seems like a bad thing either way, but for various reasons and (potentially) involved parties.
I knew a girl, who had a minimum wage job, but bought her boyfriend a $300 sweater simply to show his parents she had money.. I asked about it, and she pretty much told me it came down to "give face".
i think it is this: "面子" and as others have written, one of the more difficult concepts for western culture to fully understand.