It sounds a bit odd to be talking about 'types' of ice. But media and net articles have included enough confusion that I've decided it's actually an important point.
Ice shows up in many parts of the climate system and is generally important when it does. So I'll describe the types of ice before getting in to the confusions. (Aside: the science that studies ice is glaciology).
In the atmosphere, ice crystals high in clouds can be important for starting rain formation. Of course ice falling from the sky, whether as snowflakes, ice pellets, or hail, can be important to know about as well.
On land, one of the less well-known ice types is permafrost -- ice that is in the soil and persists from year to year. This mostly happens in very cold areas such as northern Alaska, Canada, and Siberia. For more detail about permafrost, see the National Snow and Ice Data Center's (NSDIC) page http://nsidc.org/sotc/permafrost.html They also include a graphic of where you can find permafrost. In recent years, permafrost extent has been decreasing. Since ice is a somewhat hard material, this causes problems in areas where buildings and roads were built on top of permafrost.
The two better-known land ice types are glaciers and ice sheets. Glaciers are the ice that sits on mountains. The fact that they're on sloping surfaces is important for how they move. Again, the NSIDC has an introduction to glaciers, this one aimed better towards students than the permafrost. Ice sheets are the enormous masses of ice on land. They're so big that they swamp mountains and mountain ranges. Now there are only two ice sheets -- the Greenland and the Antarctic. Sometimes we talk of the East and West Antarctic ice sheets because a mountain range (the Transantarctic mountains) runs through the Antarctic ice sheet and does fairly well separate the flow of ice. During the last ice age, there was a large ice sheet across most of northern North America, called the Laurentide ice sheet. Both ice sheets are losing mass, as are most glaciers. One reason for concern about this is that as the ice melts, its meltwater flows into the ocean and raises sea level.
On water we have three different types of ice to think about. Perhaps the oddest is ice shelves. This is ice that is floating on water, but which is attached to ice on land. The land part feeds the floating part. Several Antarctic ice shelves have collapsed into the ocean in the last few years. Icebergs are what we get when a chunk of an ice shelf breaks off. They can be as large as cities and small states or countries. The large ones, though, are in the Antarctic only. The Greenland icebergs are much smaller, though more than enough to sink the Titanic. The International Iceberg Patrol monitors the locations of these North Atlantic icebergs.
The last happens when the water freezes -- sea ice. Sea ice floats and gets moved by winds and water currents. It is important for predicting the weather, so you can see today's coverage at the NOAA/NWS Marine Modeling and Analysis Branch web page. Last fall, the Arctic experienced a record minimum in its extent at the end of the summer. The NSIDC has collected information about the record at http://nsidc.org/news/press/2007_seaiceminimum/20070810_index.html On the other end of the earth, the Antarctic ice pack has been showing a small increase in its extent, see the Crysophere Today for information about the anomaly (how much more or less ice there is compared to what's normal for the time of year) in ice coverage for both the Arctic and Antarctic. (The Antarctic is at the bottom of the page.)
So now for the confusions some have had. When our concern is about sea level, the type of ice we care about is land ice -- the ice sheets and glaciers mostly. When these types melt, sea level rises. If all of the Greenland ice sheet melted, sea level would rise about 6 meters (about 20 feet), enough to put much of Florida, for instance, below sea level. Glaciologists have observed that both Greenland and Antarctica ice sheets are melting. A research question is just how fast they will melt in the future. Most glaciers are also melting.
That's straightforward. What some have confused is 'Antarctic ice', where they're thinking about sea level changes (so should be concerned about land ice) and then looking at the sea ice instead. Sea ice has little to do with sea level. In terms of total sea ice trends, you can look again at Crysophere Today and compare how large the Antarctic positive anomaly is to the Arctic negative anomaly.
A different confusion was someone who compared the February ice cover in the Arctic (near the time of its maximum extent -- it's cold in the Arctic in the winter!) to the cover last fall (near the time of minimum coverage -- after the summer's heat had time to melt as much ice as it could). When we're looking for changes for climate, we certainly have to pay attention to what time of year it is!
If anyone says there's more (or less) ice, be sure that they know which type of ice they're talking about. Also check that they're comparing the same time of year.