Common for all of them is that they are fixed, rather than dynamic. They are used out of context. They are frozen meanings used in place of perceiving what is actually going on. They are created by the person herself, but she is no longer aware of how.
These are some classes of fixed ideas:
Fixed Assumptions - Data one assumes to be true without thinking about it, and which are never verified. Hidden assumptions.
Fixed Necessities - Something that must be a certain way, or can't be a certain way. Unspecified bad consequences are expected if certain rules aren't followed.
Fixed Assertions - Patterns of being, acting or relating that the person is perpetuating automatically. Compulsive behavior patterns.
Fixed Beliefs - Basic rules about the world that one lives by but that one isn't aware of having chosen.
Fixed Rightness - A compulsive need to make oneself right and/or others wrong
These are somewhat arbitrary and overlapping categories. Nevertheless they are useful in that somewhat different techniques might be applicable in each category.
Notice that our target is the fixed quality of these different types of ideas. It is not that there is something inherently wrong in having beliefs or desires. What we would like to establish is that the person has a choice about it, and that ideas become dynamic tools one can use or not use at will.
What we are after is something that is taken out of context, elevated to a global generalization, and never inspected.