When talking about business associates or the like, the two words have similar meanings. But "network" generally has the connotation of an organization, where "connections" means a bunch of individual people.
So if what you mean is that on various trips to Singapore you have met people whom you can call upon for favors, etc, you would say you have "connections". But if you visited Singapore and hired many people, or established offices all over the city, then you might say you have a "network". We talk about a company building a "network of sales offices" throughout a region, or a country establishing a "network of spies" in a hostile nation.
People do sometimes use "network" to talk about casual business contacts, but when they do they usually are referring to a set of contacts carefully and deliberately built up. Like someone might say, "It's not enough to just have a few connections in the airline industry. You need to build a network of reliable contacts."