In this image there are subtle differences showing that they aren't the same person. For example Gman has a widow's peak and his facial structure is more sunken in than Gordon's.
There have been endless theories as to who the G-man is. Many assume his title is short for 'Government-man', hence his formal appearance and mannerisms (e.g. always straightening his tie). A higher order is clearly present within the Half Life universe, as the G-man possesses the ability to bend and distort time and space. He constantly talks of his employers which means it is likely there are beings with power that surpasses his own.
In many instances during the Half Life series G-man both helps and hinders Gordon. His constant observation of your actions suggests he is testing you. When he supposedly traps Gordon in a room full of acid by closing the door, it is seen that he is pushing Gordon's capabilities. However on the occasions where he saves Gordon, many feel that the G-man does not want to lose such a promising subject just yet.