Some 1H weapons have an alternate mode that changes them to 2H. The fighting pick, military sickle, fighting axe, and langes messer are the only ones I remember off the top of my head. Good to use if you are a heavy crossbow/arbalest/2 slot bow user. They are typically a little stronger than their 1H modes, but still only take up 1 slot of inventory space. The only 2H category weapon that is 1 slot is the mace. In their alternate modes, the 1H weapons use 2H weapon proficiency.
Many 2H swords have an alternate mode that is called "half-swording" and is meant to be used as an anti-cavalry measure. It uses polearm weapon proficiency, and your overhead and thrust are both the same thrusting animation. It can be used to rear an incoming horse, but most people don't bother with it.
Some 2H weapons are listed as 1 handed/2 handed. This means that if you have a shield, you can wield them at the same time. In this case they use 1H weapon proficiency. Like spears, they get lowered damage and speed while you have the shield out.
A lot of this is rehashing what others said, but I felt like consolidating into a single post. Hope this helps!