It's all good - for a fuller explanation - Minor League Baseball is the full farm system of MLB and consists of 255 teams divided among 18 leagues that span 7 classifications. From highest to lowest they are:
- AAA - International League, Mexican League*, and Pacific Coast League
- AA - Eastern League, Southern League, and Texas League
- Advanced A - California League, Carolina League, and Florida State League
- A - Midwest League and South Atlantic League
- Short Season A - New York-Penn League and Northwest League
- Advanced Rookie - Appalachian League and Pioneer League
- Rookie - Arizona League, Dominican Summer League, and Gulf Coast League
*Even though the Mexican League is considered a Triple-A league it's unique in that its teams aren't affiliated with any MLB teams.
Triple-A through Low-A are considered full season leagues while Short Season A, Advanced Rookie, and Rookie are short season leagues playing abbreviated schedules.
Each MLB team has an affiliate at each of the full season classifications and at least one short season affiliate.
The classification is (roughly) a ladder with Triple-A being equivalent to the AHL, although some teams will choose to use their Double-A teams as their top farm team, especially if their Double-A franchise is geographically closer than their Triple-A affiliate (the Mets and the Marlins, for instance). Most MiLB teams aren't owned by their MLB affiliate (the exception being at the Rookie Level where ALL the teams are owned by MLB affiliates), so MLB teams will sign player development contracts (PDCs) with MiLB teams. As a result, affiliations can shift, usually in even-numbered years
when those PDCs expire.