As Chris mentions, you will need to fix your view of what a field is. It is simply mathematical way of saying "something which has a value everywhere". Depending on what type of value it has (scalar, vector, etc) we call it a scalar field or a vector field.
When you think about fields you are likely thinking about electric or magnetic fields, because this is usually the first instance of fields people encounter which are actually called fields. These are vector fields and there are a number of useful ways to visualise how they vary in space, such as field lines, which at every point point in the same direction as the vector field. This is, however, not referred to as the "shape", because what you will generally see is a pictorial representation of the field generated by, e.g., a point charge.
It should also be mentioned that there is only one electric and one magnetic field. That you sometimes will hear people refer to "the field of charge q and the field of charge Q" is that electromagnetism follows the superposition principle, i.e., you can figure out how a set of several charges relate to a field by summing their contribution.
You should also already be familiar with several other fields, which are usually not called as such, e.g., pressure and temperature. These are scalar fieds (they have only a value at each point and no direction), but not fundamental fields in the same way as the Higgs or electromagnetic fields.
