In English the connection is only etymological (dating to something like the 16th century use of the verb "to share"), but the implication is still there: To share X with others is to have less of X left for oneself, whether X is an object (a loaf of bread), or access to something (such as a computer, a car, or a mistress).*
With this in mind I find it remarkable that so many people who post digital copies of music recordings on the internet describe their activity as sharing. After all, this activity reduces neither the number of recordings in their collection nor their access to those recordings. My guess is that the pervasive use of "sharing" in this context is motivated by the desire to put a positive semantic spin on what - in the case of commercial music recordings - is essentially an immoral act. The kind of semantic spin that would be enthusiastically embraced by the OCCUPY EMI-BMG-SONY movement if there were one...**
After a bit of reflection I'm inclined to think that a semantically appropriate way to describe the act of making a digital copy of a recording available to others on the internet is precisely the verb used in the FBI Anti-Piracy Warning on every commercial DVD: distributing. Whether the digital data file you make available on the internet contains some commercial recording or an amateur video of your bar mitzvah, you are simply distributing digital copies of the recording. To call this "sharing" seems to me as semantically perverse as to call a beating administered by a loan shark's enforcer "debt negotiation".
* I refer here to sharing things (or access to things) that could be called "measurable", which automatically rules out cases where someone "shares" with others his wisdom, family troubles, or passion for sex in public places.
** Such semantic spins bring to mind a street protest I once saw in Manhattan on a weekday during business hours, when a group of unwashed, rent control-sustained social parasites (also known as "housing activists") carried signs saying HOUSING FOR PEOPLE, NOT FOR PROFIT!