what is the different between Latin American and Spanish America?
What is the difference in culture and people they way the live? If different
Latin America is another term to refer to those countries that were Spanish colonies (that would be Spanish America, although I have never heard that before) and French and Portuguese colonies together.
The current term "Latin America" was coined in France under Napoleon III in the 19th century to justify their kinship in Mexico.
Another similar term is Iberoamerica, which designates those territories formerly ruled by the Spanish and Portuguese empires.
In short, I think you should rephrase your question, keeping in mind there are 570 million people in Latin America, distributed in more than 20 countries, so you will find lots of differences (and thousands of similarities also).
Latin America is a geographical concept including the countries in the Americas whose official language is a Roman language. Thus, the region has 18 Spanish-speaking countries (Mexico, Guatemala, Honduras, El Salvador, Nicaragua, Costa Rica, Panama, Cuba, The Dominican Republic, Venezuela, Colombia, Ecuador, Peru, Chile, Bolivia, Argentina, Paraguay, Uruguay), 1 Spanish-speaking dependent entity (Puerto Rico), 1 French-speaking country (Haiti), 1 Portuguese-speaking country (Brazil).
Spanish America is the historical region where the Spanish empire ruled in the Americas. At its greatest extent, it stretched from the Mississippi and Floria peninsula to central Argentina and central Chile. Many territories in Caribe had been controled by Spain before the British and the French empires ruled. Brazil annexed Rio Grande do Sul and Uruguay before its independence from Portugal but only Uruguay defeated Emperor Pedro the first's army. The Brazilian state of Acre was Bolivian and parts of other Brazilian states (Roraima, Mato Grosso, etc) were controled by the Spanish empire.
The following shows the territory of Latin America ceded to the USA after the Mexican-US War.
The big grammar difference is the 2nd person plural is not used in Latin America and they speak castellano and don't call it español.
Nobody uses the term "Spanish America" anymore.