I'm aware that there is a difference of some sort. Does a taildragger inherently require more room than a nose gear to taxi around a corner?
It very much depends on the tail-dragger. Many vintage aircraft don't have wheel brakes at all and steer using the rudder, which has the tail wheel or skid attached to it. On these aircraft, steering is ineffective at low speeds, just like when steering a ship with a rudder. Unlike on a ship, you can increase your steerage by adding a burst of power and using the slipstream over the rudder to push it sideways. Very experienced pilots can turn almost on the spot at very low speeds this way, but in a tricky situation it's a judgement call whether to make a wider turn at low speed or add power and risk speeding up. For this reason it's good to have a little extra room, to make sure you can stop completely at any point and still have room to make the turn.
Dan Pichelman makes a good points in the comments. If you take a tricycle and a tail-dragger with the same turning circle, and look at the tyre marks on the ground, the tail-dragger's marks will be much bigger. That tail wheel right at the aftermost point traces out a huge circle, while the tricycle's wheels are very close together. For this reason, you need the whole turning circle to be free from obstacles such as edge markers and lights, while a tricycle can do a full turn with its tail overhanging any obstructions.
One more taxiing issue is visibility. Tail-draggers (again, especially earlier ones) are nose-high on the ground, and the engine cowling tends to prevent the pilot seeing straight forward. There have been many incidents of tail-draggers taxiing right onto smaller aircraft or obstructions straight ahead of them. (It used to be very common with Spitfires.) To avoid this, pilots are taught to weave as they taxi, so they can always check the ground ahead by looking either side of the nose. (Think of it like the clearing turns you make on a long climb.) While a tricycle might go straight along a taxiway it can only just fit into, a tail-dragger wants a much wider taxiway so that it can weave like this. You also need to plan how you're going to make the weave go into a turn when you reach a corner: if you got to the corner as you'd weaved right over to its inside, pointing towards the outside of the corner, you'd need much more room to make the turn.
For all these reasons, while it's entirely possible for a good pilot on a good day to make turns just as tight as a similar-sized tricycle aircraft, it's a good idea to allow a larger unobstructed space on straights and corners if you're expecting tail-draggers, especially students.