A walk-up is an apartment in a building that lacks an elevator.
A walk-in is a person who comes into an establishment without an appointment or without having phoned beforehand. A walk-in order is an order placed by such a person. Many different kinds of establishments refer to "walk-ins" to describe some of their customers: health clinics, car dealerships, restaurants, spas and salons, and so forth.
You can walk up to the counter and place an order. But such an order would be called a counter order, not a walk-up order.