A uniform in basketball are the jerseys and shorts worn by teams to differentiate opposing players from each other on the court. This also includes matching socks and shoes that correspond to team colors.
Players in high level leagues including the NCAA and the NBA must follow strict guidelines that limit what they can wear. All uniforms must be consistent for all players on a team, which includes jerseys, shorts, and socks. The NBA recently changed the rule that prohibited players from wearing shoes that were a different color than their team's colors, so as of now players can be creative and wear whatever color shoes they want to. Some items that are optional but allowed include headbands, sweatbands, goggles, and arm sleeves.
Casual basketball uniforms are nothing like what the pros wear. While pros have to adhere to strict policies, everyone else can wear what they want. Although most casual players look quite similar, there is nothing saying what you can and can't wear. The most common get up would be a comfortable t-shirt or tank top, baggy basketball shorts, and basketball shoes. The shoes however do not need to be super expensive ones like the pros wear, however you should make sure you have the correct shoes for the surface you are playing on, either outdoor or indoor.