There are many different varieties of spanish spoken throughout the world. what are these different ways of speaking the same language called?

Acentos y Modismos

Explanation: While the language and the rules are the same, the Spanish spoken in Argentina may sound "different" than the one spoken in Chile or in Spain, even inside of the same country, different regions may sound different, for example, the Spanish from Córdoba (Arg) sounds different than the one from Buenos Aires (arg)

Those little differences in the pronunciation are called "acentos" as:

"Acento español, acento chileno, etc.."

Other differences are the "modismos", little words that come from a cultural background dependent on the country, so the modismos in Uruguay may be different from the ones from Mexico.