My hardware provider said that he will put esonic mother board as my chipset. I only know is that it's intel g31 +intel's south bridge. Does it make any difference in performance if the poducer is different but what they produce is same?
Well technically it could make a difference, but you probably won't notice much. As long as the specs match exactly, they will act almost identical.
Most Mother Boards as long as they are the same socket (work with the same CPU) with general run at the same speeds. Mostly you have to pay more for extra features and options, i.e. more connectors or on board audio. In some cases the overclock options are limited, but for the most part buy the brand with the best warranty and user rating.
Intel boards are generally what you would call "stock" i.e. they have the features than Intel includes with their chipset, but nothing else. Other motherboard manufacturers offer more features and/or lower prices than what intel sells. It really depends on the manufacturer's reputation more than it's not an Intel manufactured board.