The term "Latin America" implies the ancient construct from the Old World into the New. Both Spain and Portugal where made up of various tightly controlled provinces during the Roman Empire. If "Latin America" describes where the Southern European states of Spain and Portugal settled in Central America, I wonder why the equivalent "Gallo or Germanic America" never came to be used to describe the settlement in the New World of Northern European states.
In early colonization, say from 1500, the difference between Latin America and its European parents was slight. Colonies were considered to be part of the Mother Country, not subordinate satellites, a concept which came a bit later as those areas became exploited.
The Latin versus Gallo-Germanic terms are not merely semantics; those areas of Europe under Roman rule became the most heavily influenced by the remnant of the Empire, the Catholic Church. Those areas where Rome never fully penetrated is where the Protestant Reformation began -- and the political and cultural changes that altered the Old World, then the New World. It's curious that the religious and political upheaval of the Reformation nearly coincided with the Age of Exploration in the early 1500's, and the settlement of colonies from Europe followed suit. The Northern versus Southern European influence (ie., the opposition of language, religion, and politics) in the Old World played out in the Northern versus Central and Southern America of the New World.
To which particular time period are you refering? If you are talking about colonial times, one of the major differences was that Spain and Portugual had attained a different level of civilisation, incorporating such aspects as reading, writing and the use of gunpowder that meant they were superior in certain ways to the Latin American societies that they conquered.
I, too, agree with pohnpei. The influence of Catholicism in Spain, Portugal, and Latin America has historically been very strong. Interestingly, I have been reading about a great growth of evangelical Protestantism in Latin America, but I have heard about no such growth in Spain or Portugal. Here, then, may be a way in which a similarity has begun to change into a difference.
I have to agree with pohnpei. The influence of the Catholic Church was similar in the areas mentioned. Outside of that, the main differences are the multiple cultures which are represented within specific countries. Not unlike many countries, a person's origin (exact location of birth/growing up) influences how others look at them.
Latin America is a cultural term, including a great many countries located in Central America and on the South American continent. Because most (but not all) of these countries were originally colonies of Spain or Portugal, they share many cultural characteristics - language, religion, music, art, foods, and so forth.
Europe is a continent populated by many different countries having widely varied cultures. There are differences in all of the characteristics mentioned above between at least some European countries and some Latin American countries.
The major similarity I see with the Iberian countries (and to some degree with places like France) was the great power wielded by the Catholic Church. The Church had significant economic, political, and social power in all of these places.
The major difference I see is in the fact that social status in the Latin American countries was determined largely by place of birth. Any person born in the Americas was automatically inferior to people born in Europe. This particular way of ordering society did not, of course, exist in Europe.