Before each game, the Umpires take some earth and rub it into the baseballs to remove the shine on the new baseballs. Only new balls are used for a game. Makes the ball easier to see. Used balls are retained by the home team and used for practice.
The "ball girls" retrieve foul balls (out of play) before they reach the stands. At the end of each inning, they give them back to the umpire who determines if they are still fit for play. If yes, they are returned to play, if no, they become practice balls. The umpires are required to have 144 balls ready for each game. Only one ball is used at a time.
There are two leagues, the American and National. The American League uses "Rawlings" balls, the National uses "Spalding". The dimensions and specifications for both balls are identical. In fact, they are both made in the same factory. Half are stamped "Rawlings", half are stamped "Spalding".