I suppose that Chinese people use the term 点心 to indicate a variety of small bite-sized portions of food which could pass as "snacks" due to their small size, unless you order many of them, of course. 点心 usually come in the form of dumplings, steamed buns, meatballs, rolls, and are generally served in small steamer baskets, there are many types of "dim sum", not just one. Am I correct? Most likely some English speaking Chinese would use the word "dim sum" referring to snacks, but I doubt native English speakers would understand what they mean. A snack is a generic term to describe a small portion of food eaten between meals. It can be anything that's small enough not to be considered a meal. You can have dim sum as snack. But it's not correct to say that fast food is a type of snack, here is why: "Fast food" is used to describe food prepared and served very quickly. It has nothing to do with the size of the dish. Fast food is McDonald's to give you an example. You can order a large quantity of food, but the difference is: it's precooked by the time you order it and can be also packed as take-out. Therefore you don't have to wait, hence the adjective "fast".

In Australia, "dim sim" is a kind of fast food, and a mutant spawn of dim sum. It's meat in pastry, usually deep friend but sometimes steamed. We still cover it in soy sauce (or, tomato sauce). It is second in horror only to the Chiko Roll (another Aussie mutation of proper Chinese cuisine). Snack doesn't mean fast food (in the common understanding). A snack is just any small, quick-to-make meal. It could be an apple. (Or a dim sim.)

In Ireland, I have never heard anyone refer to a snack as dim sum. Also snack would not always mean fast food. If someone said 'I'm going for a snack, do you want to come?' most people would interpret this as the person wants to go get some light to eat. I mean 'light' in this sense as something that is not as heavy on the stomach as say 'A full roast'. A snack would refer to things like sandwiches,wraps,rolls etc.

I understand that in China, dim sum was served just until mid-afternoon as a snack. That has changed in modern times. In the U.S. a dim sum restaurant always serves it as a full meal. I like it very much, but if I go to a dim sum restaurant in the U.S., I would expect to eat a large meal, not a snack.