Definition:Conflation

Definiiton
A conflation is a mistake in which two or more separate but similar ideas become confused with one another.

Example
The trivial quotient on a set is the mapping $$q_{\Delta_S}: S \to S / \Delta_S: $$ defined as:


 * $$\forall x \in S: q_{\Delta_S} \left({x}\right) = \left\{{x}\right\}$$

This can become conflated with the identity mapping $$I_S: S \to S$$ defined as:
 * $$\forall x \in S: I_S \left({x}\right) = x$$

The image of an element under the identity mapping is that element.

The image of an element under the trivial quotient is a singleton set containing just that element.

The two are completely different.