Hi anirudh316 -- good questions!
The 1-year MBA is more common in Europe (they're typically a bit longer than that, like 16 months or so), and they're geared more towards people further along in their careers, with extensive work experience - 5 years is average. These are schools like LBS, INSEAD, etc. By their nature, they offer a more "international" experience because of their location and the students that they attract. They tend to be more diverse than US programs and many of them have a language requirement (you need to demonstrate proficiency in a new foreign language when you graduate). These schools generally do not offer an internship (some tracks do, for example the INSEAD January start can accommodate one) and they can be a little more challenging for someone to use as a vehicle for a drastic career change.
Conversely, the two-year full-time MBA is ideal for career-changers (though it's also well suited for any type of career transition or development). This is because of the summer internship opportunity between the first and second year. This two-year program is the most common MBA offered by the top American bschools. Students tend to be younger than in Europe, with average age typically around 27. Some schools are more open to younger candidates, including Harvard, Booth, Yale, a few others. The three years of experience that you currently have would position you perfectly for any of the American programs, you're right in the sweet spot.
There are a few accelerated full-time programs in the U.S., notably the J-Term at Columbia which is the same MBA but without the summer internship; and Kellogg has a 1Y MBA for people who studied the standard core subjects in undergrad. Cornell also has a fast-track MBA for similar candidates.
All U.S. programs appreciate candidates who have international experience, but it's not required for admission. You would have the opportunity to do a study-abroad or an internship overseas if you wanted; at some schools, like Stanford, an international experience is now required of all students. You can expect a third of the students to be foreign (non-US citizens) at most of these American programs; schools like Columbia and Wharton tend to be even higher.
The term "international MBA" could mean lots of different things. Wharton for example has the Lauder program which is a joint MBA/Masters with a focus on international studies; many other top bschools have other dual-degree or partner programs with their international affairs schools etc. In all bschools you can take classes focusing on global trade, enterepreuneurship in developing countries, etc etc etc. So much of it depends on what you literally want to study, in terms of what you want to do with your future career.
Basically, there are a lot of options!
