In machine learning and pattern recognition, the term feature space refers to two related, but distinct notions.

The Lebesgue measure is often denoted dx, but this should not be confused with the distinct notion of a volume form.

There are several related but distinct notions of central product.

Many distinct notions of prosperity, such as economic prosperity, health, and happiness, are correlated or even have causal effects on each other.

In mathematics, the term lattice group is used for two distinct notions:

There are two distinct, but closely related, notions of bundle map, depending on whether the fiber bundles in question have a common base space.

Note that there are several distinct notions of "identity" being referenced here:

I don't know, but I have the distinct notion he's going to think I was responsible for getting the play's director to notice her.

In mathematics and physics, there are various distinct notions that are referred to under the name of integrable systems.

There are two distinct notions of multiple edges.