This is an interesting and complex question. I hope I am able to give you a satisfactory answer. To transition between one state and another, something has to change. Remember your Ideal Gas Law. P=nKT or PV=nRT.
Different substances will have different strengths of their intermolecular forces that are acting on the molecules and atoms of the substance, which means that they have different limits to change phase.
We know that energy moves in one direction, hot to cold, and this is not instantaneous. This video shows a soap bubble going from a liquid to a solid. https://www.youtube.com/watch?v=52xFz1Cn8E8 In the bubble you have two different states, some of it is still liquid whilst parts are solid until it is all frozen. You can see two aspects of this, the growth of the ice crystals as they eventually seed and completely cover the bubble and the initial part where we have a few random ice crystals float to the top (ice is less dense than water).
So to go from liquid to solid or vice versa we have to overcome the molecular forces by a transition of energy to break the bonds. The transition is less of a grey zone, but more this energy transfer between states whilst the substance as a whole we are waiting for the majority to change to call it either a solid or a liquid.
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