I know that 东西 translates to "something" in English.
So I would like to know, can both 一些东西 and 一点东西 be used? If so, what are their differences in meaning?
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Yes, 一些东西 and 一点东西 are both OK. 一些东西 means something that the quantity can be either many or less, while 一点东西 means something but not many.
You can say both, but they apply in different situations.
一些 means a small number of countable things. Use it when you would say "some" or "a few" in English.
一些蛋糕 "some cakes" is appropriate to talk about three or four cakes in the bakery window.
一些汽水 "some sodas" is appropriate to talk about a few cans of soda on the table.
一些自行车 "some bicycles" is appropriate to talk about some bicycles outside your school.
On the other hand, 一点 means a small amount or "a little bit" of a "mass noun".
一点蛋糕 "a little bit of cake" is appropriate to talk about a portion of a single cake.
一点汽水 "a little bit of soda" is appropriate to talk about how much is left in your glass.
The difference is very clear when you try to say 一点自行车 since a bicycle cannot be portioned out "a little bit" at a time.
tl;dr To make it easy to remember, if you can count how many you have (apples, kittens, phones, etc.) then use 一些, otherwise, go with 一点。
一些means "some", but 一点 means "a little".
In math, 一些東西 is more than 一點東西.
Just like "some" is more than "a little".
I've been studying chinese for a couple of years and this is the most difficult subject I have bumped into with difference. It's like a stone in the road I can't jump over. All those answers are right in a superficial and practical level but implies a western approach to something far more complex.
Many natives have told me that chinese people don't make a distinction between countable or uncountable nouns, and that I should approach the subject of indefinite measure words with a chinese mind. 一点 doesn't always means "a little" of a mass noun. It can be used sometimes with countable nouns in english like for example "advice" (一点意见 = a few advices, not a little bit of advice) but we can't say 一点锚 (some cats). That would be incorrect. Which leads me to think that chinese DO really make a distinction between countable or uncountable things (ok, maybe this way of naming it is misleading as everything can be counted with it's appropriate number and classifier, let's called them common nouns VS material nouns, or individual nouns VS mass nouns, whatever...)
On the other hand, you say that 一些 means "a few", but it can also be used with things that for an english speaker would be mass nouns like sand, water, gold or rice, (like "a few waters!") in the same way we do with 一点. So, the boundaries between countable and uncountable nouns seem to be quite blurred and confusing and I still find some inconsistencies even when I try to think as a native chinese.
I would read those as "several things" and "a bit of stuff", respectively. As others have noted, 一些 is almost always used with a countable noun and 一點 is typically (though not quite as universally) used with a mass noun. The situation for the latter phrase is not that different from the confusion between "fewer" and "less" in English; although "less" should not be used with countable nouns, you'll find it (and 一點) used with them anyway, from time to time.