Super-cooled liquids
When a liquid is supercooled its structure doesn't change significantly, only the particles have less kinetic energy available. As you cool even further, it could occur that particles get caught in local minima and eventually you'll end up with a glass, which can be thought of as a frozen liquid structure. As particles are trapped it will resist shear in an elastic fashion so you have a solid. In this regard it is a barrierless transition. There is no interface whatsoever.

Crystal formation is fundamentally different as the local structure changes first to form a nucleus. This has both energetic and entropic consequences and the aforementioned kinetic barrier is observed. I would also like to add that crystal nuclei are formed all the time but they don't reach the critical size if the temperature is too high.