There was a minor league team called the San Diego Padres of the Pacific Coast League that was in operation from 1936-1968. When Major League Baseball expanded to San Diego in 1969, the old nickname was retained for the new San Diego Padres.
That minor league franchise won the PCL title in 1937, led by 18-year-old Ted Williams, the future Hall-of-Famer who was a native of San Diego.
Though it has no sports connection, the name Padre was taken from the Spanish word for "Father", a term of respect used for Spanish missionaries. Padres refers to the Spanish Franciscan friars who founded San Diego in 1769.
The team is frequently called the "Pads" or "Pods" in the media, which rhymes with the first syllable of "PAHD-rays". "Friars" has also been a longtime team nickname.