Commerce is generally accepted to mean the mutually agreed upon and fair exchange of value being mutually beneficial to both parties. Human society greatly depends on 'quid pro quo' or something for something interaction.
A gift or a present is the transfer of something without the expectation of receiving something in return. Although gift-giving might involve an expectation of reciprocity, a gift is meant to be free. Generally gifts are given either as a show of thanks or as a means of enticing the other party into more exchanges through a show of generosity.
Theft is the taking of property or services without consent or without the agreed upon compensation thus permently depriving the other party their property or the enjoyment of the fruits of their labors. It should be noted that intent is a large part of theft. It is possible to take something while under the impression that the property or service was due the taking party but this does not excuse depriving of the second party of their property. That is to say if party A finds a cake and thinks 'oh how nice, someone remembered my birthday' and eats the cake and party B comes along and says 'where is the cake that I was taking to my mother?' party A is liable to replace the cake. Failure on party A's part to provide just compensation for party B's lost becomes intent to permanently deprive party B of their property. The providing of cake ingredients would not constitute fair compensation for the same reason that a pile of building materials would not substitute for the loss of one's house.