Why do some words have different names in different countries? For example, "weather" is called "tiempo" in some countries, and "clima" in other countries.
Maybe it would be better to think about communities instead of languages. Spanish is a single language but a language lives fully only while it's spoken by people; it's not a monolithic abstract thing with strict rules that everybody obeys. People innovate: they make new words from others that exist already in the language, they take words from other languages, etc. People copy other people's new words. But people who live far apart don't get to hear other people using these new words, so they keep using other words (and invent their own, which in turn aren't copied by those who live far away from them). So language communities form and, although they might share the same ground rules and basic lexicon, a lot of variation among them appears and persists.
I don't think clima and tiempo are differently used in different countries. As far as I know people use both. Clima has a technical meaning that makes it different from tiempo (just as climate and weather in English), but people mostly ignore it and use both interchangeably, in every Spanish-speaking country.