The correct way to connect a procedural or B&W texture using a Displacement node is like this (no need for the Normal Map node - that is reserved for data from a "proper" normal map such as the purplish looking bitmap images I've sure you've seen):

However, if you are using EEVEE, or are only looking to generate the look of displacement (without needing a heavily subdivided mesh), you will probably find it works just as well to connect the texture through a Bump Node, and using it's output as Normal data:

To answer your second question - there is really no difference between a mesh and a model (two ways of describing the same thing), however some people might use the word model to imply a fully finished product (not just a mesh, but a textured mesh, or a mesh rigged for animation, etc...)