Best to start with Chapter one of our rule book:
1F4. Club Membership
(a) Licensed riders must register with a club and USA Cycling before they are eligible to present themselves as a member of that club. This includes, but is not limited to wearing a club’s jersey or entering a race as a member of the club.
(b) Riders are only permitted to be a licensed member of one registered club per discipline, which is shown on the racing license.
Registered clubs may register one or more race teams. Teams may be based on factors such as discipline, gender, region, class, and sponsorship.
1F6 Race team membership
(a) Riders may belong to a racing team. Generally this is a team organized by their licensed club, for which they compete throughout the season. However, riders may be on different racing teams for particular disciplines (road, track and cyclo-cross), including teams organized by other clubs.
(b) A rider’s team affiliations must be registered with USA Cycling and will be shown in USAC member data, either on the racing license or on the USAC website. Riders whose team affiliation is not printed on their license should be prepared to show documentation at registration.
A club is the group of cyclist registered as an entity under USA Cycling. Generally, a team is a competitive or specialized subset of the club. An example would be a junior development team or a women's team. Certainly, some clubs are also teams if they don't have sub groups.