In the simplest terms, iceberg water comes from icebergs floating in the sea, and glacier water is meltwater from land-based glaciers. The original source of both is a land-based glacier, but all glacier water brands on the market have had some form of contact with the ground, while iceberg water has not.
The longer explanation begins with saying that no, iceberg waters such as Svalbarði are not the same thing as bottled waters labeled glacier water. Glaciers are sheets of ice covering large areas of land, though occasionally with extensions that sit on top of water. Glacier bottled water brands are sourced from water that has melted off those glaciers and is then gathered after passing either over land or into the earth. They may be tapped from surface water such as rivers or lakes, from springs that come to the surface after the meltwater has initially gone underground, or from wells drilled down to aquifers where the meltwater has become trapped. In essence, these are waters which typically fall under normal spring, mineral, artesian, or surface water categories. The only difference is that the water originally melted off a glacier. Otherwise, they run through the same ground-contact processes which may cause infusion of minerals or possible exposure to man-made pollution.
Iceberg water on the other hand has never touched ground. After originally falling from the sky as snow and compacting into a glacier, it has stayed as ice for potentially thousands of years. Many glaciers - including in Svalbard - move over time and eventually reach the sea. When they reach the sea, ice breaks off the glacier in a process known as calving. That is where a glacier becomes a newborn iceberg floating in the sea where we can gather them. By knowing the signs to watch for, we can tell which ice has been preserved in the center of the glacier and never touched ground since it first fell as snow.