"Contemporaneous" vs "simultaneous"

I've done a bit of searching but cannot find a definitive distinction between contemporaneous and simultaneous. I personally use the words interchangeably. Am I correct in doing so?

The OED gives these definitions, which look pretty typical to me:

Contemporaneous: Belonging to the same time or period; existing or occurring at the same time.

Simultaneous: Existing, happening, occurring, operating, etc., at the same time; coincident in time.

So "contemporaneous" refers to things that happened in, or are associated with, the same period of time, whereas "simultaneous" refers to things that happened at the same moment.

To put it another way, contemporaneous things were happening at the same time, while simultaneous things happened at the same time.

Contemporaneous implies things happening during broadly the same period of time. Simultaneous conveys a greater sense of things happening at exactly the same time.

Contemporaneous things, to my mind, normally relates to things that happened in the past at around the same time, for a reasonably sustained period of time.

Simultaneous, to my mind, is less time-specific and is more likely to apply to things that occurred for a short period of time.

Two guns might be fired simultaneously; scientists might have worked contemporaneously.