At in person events, teammates are not paired against one another, if possible. (Per TCA guidelines, players who train with a school chess club but do not attend that school cannot be considered team members in TCA sponsored events.) In most tournaments, teams are defined also by the section in which the team is participating, e.g. the same school could field two teams at the same tournament – one in a K-3 section and one in a K-6 section. The top 4 players in a section are used for determining a team’s total points, but all team members are considered ‘part of the team.’ At some tournaments the organizer might allow a school to break it’s players into multiple teams within the same section, but those different teams could possibly be paired against one another.
Online events are a bit different. Some systems allow for teams to be declared, and some do not. Please review the tournament description in question to see if teams will receive awards and whether teammates will be paired against one another.