Separations of Divisions are determined by number of scholarships offered, number of sports offered, recruiting rules among other characteristics.
Enrollment does not determine level of competition.
On the whole, DIII schools tend to be high achieving academic schools, however these types of schools can also be found at all levels and are not exclusive to DIII.
In some sports (like wrestling), the various levels can compete against each other with varying results (both in season and as exhibitions).
NAIA is a separate governing body with different eligibility and recruiting rules.
Junior College is usually for 2 years, can be very competitive and provide athletic development, be academically challenging, be socially fulfilling, cost less and lead to an opportunity to successfully transfer to a 4 year school.