The Longhorns and the Sooners are big rivals
Varsity is the team you play for when facing another school. Intramural is the team you play for when you face teams of the same sport with only students in your school.
Up until the mid eighties freshman played on a junior varsity team and upper class man played varsity on the collegiate level.
At most high schools, juniors are allowed to play on junior varsity teams. If you are good enough to make the team, you should be able to play.
There are 13 Colorado sports teams and 8 college Colorado sports teams
Certainly, they can. The qualification "varsity" occurs when a team is regularly engaged in competition with other teams from other schools in recognized leagues or associations of whatever sort, as in varsity soccer, football, baseball, etc. Oftentimes, the younger or weaker players from popular varsity teams are themselves organized (or are selected for) a "junior varsity" team. These weaker or younger teams then play the weaker or younger players from other schools and the upshot is "junior varsity" competition. However, nothing requires the school that sponsors a varsity team to have a junior varsity team; it is just traditional, especially amongst larger and more established high school programs. When there is no varsity team, you sometimes have "club" teams where members compete with other school clubs (but almost never with other varsity teams of the same sport) in more informal matches. Such club teams are even sometimes recognized as having won "championships," but these are less trusted honors, because of the small number of schools that participate, and the often unofficial rules that govern them.
just college teams
college sports but no national teams
No, especially if one of the teams is a varsity team.
The name of the sports teams at The College of Wooster is the Fighting Scots.
If you are talking about national sports no college yes