When you go into a tournament, take the Eudora Cardinal Conflict for example, and you go to teams and choose your team... Why, within a team, are there scoring and non-scoring team members?

It just depends on how trackwrestling is set up to score the tournament. Often times a wrestler only earns team points if they place, so if they don't place they would have scored 0 team points. Every tournament can use different criteria for how they score team points and it just depends on how the tournament host sets it up. Sometimes a wrestler can score more points for a win by pin or tech fall or major decision than a regular win. Sometimes they give advancement points for moving through the bracket. But that is why some members are scored and some are not.

For the Eudora tournament, each club could choose 2 wrestlers from each division to score for their team. In this case, this is why some are "scorers" and others are not.