In my opinion, the big difference is in one pronoun and how it be conjugated according to the verb.
In the second plural pronoun, the Spain people use "vosotros" meanwhile people from latinoamerica use "ustedes", Similarly the verbs changes acording to the noun.
If you want to conjugate the verb "to walk = caminar" , will be like this:
Vosotros Caminais ----Ustedes Caminan
Vosotros Caminasteis----Ustedes Caminaron
Vosotros Caminareis-----Ustedes Caminarán
the other pronouns are conjugated without variation between both regions
and the other differences are the means of some words