No. Consciousness is the waking self, the ability to perceive at all in a sober and non-dreaming fashion. With regard to consciousness the ability to perceive at all is sufficient regardless of whether that perceptive ability is limited to yourself, a narrow subject, or details around you. The oppose is unconsciousness, which is typically thought of as the sleeping mind.

Conscientiousness is more distinct, a subset. It is the fine detail by which a person can perceive dates, times, and schedules. Other facets of conscientiousness include social intelligence, empathy, organizational capacity, cleanliness/orderliness, details about nature, comparisons and measures, and more.

Low conscientious people struggle to think beyond themselves and struggle to find the energy to perform tasks not considered immediately pleasurable or self-rewarding. That is what makes the costs of abstract task completion so very expensive, because the effort required is beyond consideration. For example a simple task like cleaning your room or waking early without an alarm clock is an impossibility for some people and for others it is as effortless as getting dressed. For people who struggle with these they appear more comfortable with complexity or disorderly, which is a false conclusion. These disordered result may be very stressful and perhaps over stimulating, but the effort to correct for it is too expensive to resolve. That is why some programmers can seem to build anything and refactor large applications in a few hours while other developers struggle to merely formulate a starting idea in that time and an equivalent refactor would take weeks to accomplish.

Extremely low conscientiousness is linked to a variety of mental and behavioral health disorders because it is so completely detrimental to standards of living and real world performance. Extremely high conscientiousness is linked to perfectionism, OCD, and anxiety in a world of disordered imperfections.