Either, and they mean slightly different things. The threshold is the metal, wood, marble, or other strip of material that joins two flat surfaces, often different types of flooring or floor covering, or the switch from outside (dirt, grass, gravel, brick, cement, etc.) to inside. You can stand at it, and if it's appropriately sized, on it.
My house has a wooden thresholds about two inches wide separating carpeted areas from wood flooring, and metal strips smaller than that separating carpet and tile. But the bathrooms have marble thresholds about eight inches wide, easily stood upon. My previous house, built between 1910 and 1920, had its faults, but great big thresholds of twelve inches wasn't one of them. I bet as you go back in time to older buildings, they get even bigger.
Maryn, at the threshold of cleaning the bathroom