Latin Americans have taken their language not precisely from Castile, but from other regions of Spain, mainly Andalucía, which made them not talk the same way than modern day Spaniards.
As for localisms, Latin American Spanish is very diverse; things get dubbed in many different places such as Mexico, Miami and Colombia, and because of that they actually have to make an effort to keep neutral.>>37363624
Argentina and Uruguay uses different conjugations for second person (vos fuiste v/s tú fuiste) while European Spanish uses "vosotros" as plural second person, while Latin America uses "ustedes", complete with different conjugations (vosotros sois v/s ustedes son)
Latin American Spanish in general tend to use another past tense conjugation than European Spanish (yo fui v/s yo he sido)
We understand each other, however.