The halberd consists of an axe blade topped with a spike mounted on a long shaft... It is very similar to certain forms of the voulge in design and usage. The halberd was 1.5 to 1.8 meters (5 to 6 feet) long
The pike was an extremely long weapon, varying considerably in size, from 3 to 6 metres (10 to over 20 feet) long... It is a common mistake to refer to a bladed polearm as a pike. Such weapons are more generally halberds or glaives.
As my guide on vanilla pike deployment and formations can attest, I'm somewhat of a pike fanatic in vanilla Medieval 2. So forgive me if I'm being somewhat of a stickler for semantics here, but the descriptions of some of the Third Age Total War units are rather... misleading.
Because of my love for the Italian states in medieval 2, I started up a Rhun campaign, basing my decision on the fact that somewhere up along the tech tree, the Rhun got "elite pikemen". For instance, this little gem from Honga.net:
Quite literally the bite of the Lôke-Khans army, the Lôke-Gamp Rim are highly trained
pikemen and swordsmen.
So I said to myself: "Ooo. A pike faction. I gotta try this." To my horror, I climbed up the tech tree and found myself utterly disappointed by the Lôke-Gamp Rim for this simple fact:
Lôke-Gamp Rim are halberdiers, not pikemen.
Needless to say, I went on and finished that game, but it didn't have the delicious Italian flavor I was hoping for (Then I went and picked up Isengard, which satisfied my craving for Italian pike maneuvering).
As it stands, there is only a single TRUE pike unit in TATW, and that happens to be Isengard Uruk-hai Pikemen. The weapon the Lôke-Gamp Rim carry is considered, by tactical military historians, more of another form of polearm, closer to Halberds than anything. By definition, halberds were characterized as bladed polearms with an axe head that could be swung to punch through armor and a thrusting spearhead, whereas pikes were actually just really, really long thrusting spears.
Also, consider the weapon carried by the Rhun "pikemen" is much, much shorter than a real pike would be:

You can really see the discrepancy between Uruk-hai pikes and Lôke-Gamp Rim "pikes" here.
Looking through the other unit listings, the same sort of incorrect semantics continues into Eriador's Greenway Guardsmen, who are also referred to as pikemen but have the same halberd-class weapon as the Lôke-Gamp Rim.
I would very much like to suggest a change of the unit descriptions, to more accurately reflect their real unit weaponry, and as such would require merely a minor modification in the text description files of the Lôke-Gamp Rim and Greenway Guardsmen.