The Trench Knife is a straight upgrade from Nova's Shank. Like the shank, it deals out an average amount of damage per hit. The weapon strikes quickly, on par with the shank, with the relatively low damage being a minor problem due to being able to strike several times where a knife would only manage a single swing. However, the Trench Knife has better range.
The Switchblade released in the later Golden Grin Casino DLC has nearly the exact same stats as the Trench Knife, but with a faster unequip delay and an earlier unlock level, at 24, obsoleting the Trench Knife.
A trench knife is a type of blade that was specifically designed for trench warfare, often intended to be used as a thrusting or jabbing tool than a slashing one. Some of the more famous models even had integral brass knuckles.