ugh, I've been trying contribute to this for a day and half but the site kept logging me out when I tried posting...
Visual communication and information hierarchy
Concept design is about effectively communicating an idea or concept through drawings to a client (customer, development team, model render etc). It doesn't need to be super polished, it just needs to present enough information that they get the gist of the personality, mood and/or purpose.
Illustration is storytelling through a limited setting, you get one image to explain it all. Concept design is also storytelling, but it allows a broader level of detail to be examined, since it is not limited to a single scene.
When it comes to details, what's expected will vary on the nature of the project (a 1st-person racing game will have different deliverables than a 360° 3rd-person adventure game).
Information hierarchy is how you determine what are the key factors, what is essential to convey the idea so that a client will 'get it' by looking with little to no verbal explanation.
This is true in all Design, not just Concept but don't limit yourself to digital medium. Inspiration can strike at any moment, and conversations with clients might not always happen near a computer. The ability to quickly and visually communicate an idea with them can be as simple as a pen & napkin drawing.
If you're concerned about rapid ideation, that it takes you too long on a concept sketch, try this: it's a drawing exercise to teach how to prioritize core details of an idea or object versus the polish that can bog us down (like drawing every scale on a mermaid character).
Do a still life/drawing study of an object in your house (not an apple, something with a little more detail like a car or a shoe), or take a previously refined concept you have.
Take 3 hours to render it up, use whatever medium your comfortable with and give us as much detail as possible.
Next, draw it again, but this time in 30 mins.
Do it one last time, but only in 3 mins.
The commitment to detail should get simpler with less time, but it should also make you consider what is essential in conveying this idea or object to us.