El deporte

Jugar is to play a game. Tocar is to play an instrument. They are not interchangeable and swapping them is the single most recognisable error an English speaker makes in this area.

Toco la guitarra. Juego al fútbol. Toco el fútbol would mean you touched it.

Tocar also means to touch, which is where the instrument sense comes from, and to be someone's turn: te toca a ti.

jugar takes a

Jugar al fútbol, jugar al tenis, jugar a las cartas. The preposition is not optional in Spain, though it is often dropped in parts of Latin America.

Jugar is also the only verb in the language with a u-to-ue stem change: juego, juegas, juega. There is exactly one, and this is it.

The many words for a game

Juego is a game in general, and play as an activity. Partido is a match, a fixture between two sides. Partida is a game of cards or chess, a single round of something. Jugada is a move or a play within a game.

English uses game for most of these and lets context sort it out. Spanish would rather be specific.

ganar and perder

Ganar is to win and to earn, which you met with money. Perder is to lose, and also to miss: perdí el partido is ambiguous between losing the match and missing it, and only tone will tell you.

Empatar is to draw, and it is a word English football commentary needs and does not have as a single verb.

Three words for a ball

Pelota is a ball, generally, and the default. Bola is a ball that is solid or round in a more geometric sense: a bowling ball, a snowball. Balón is a large inflated ball: football, basketball.

So a football is un balón, a tennis ball is una pelota, and a cannonball is una bola. Nobody will correct you, but the distinction is real and native speakers keep it.