I'm not an expert on this, but as a Singaporean, here are some factors off the top of my head (plus some Googling), explaining why Singapore is different from other first-world countries (in terms of revenue and expenditures).
- In 2014, the personal income tax contributed only about 14.6% of government revenues (Source). In contrast, in Canada for example, it was nearly 48% of government revenues (C\$135.7b out of C\$282.3b in 2015).

- One unusual revenue source deserves commentary: car taxes, including the so-called Certificate of Entitlement (COE). The COE is simply a piece of paper that entitles you to own a car. This recent news story mentions how the COE price hit a 5-year low, at "only" S\$45,002 (≈ US\$31,600) for small cars.
These COEs ("Vehicle Quota Premiums") make up 6.0% of government revenue.
Besides this very expensive piece of paper, a car-owner still has to pay all the other usual taxes (GST, road taxes) and insurance, plus a lot of unusual fees (e.g. Electronic Road Pricing - an idea which London borrowed). A lot of these flow to government coffers. Together, these make Singapore easily the most expensive place in the world to own cars.
- "Public" housing is not cheap, heavily-subsidized housing.
It is true that over 80% of Singapore residents live in government housing (HDB flats). But these are not the sort of heavily-subsidized public housing you have in some Western countries. Indeed, it is a frequent gripe amongst Singaporeans that these are incredibly expensive and there are often conspiracy theories that the government sometimes actively works to push up prices.
Given the lack of transparency and also the fact that Singaporeans are actively encouraged to use their CPF (retirement) savings to pay for these homes, these conspiracy theories are not without merit.
Government housing is generally priced at market rates. For example, recently a 1,001 square foot flat went for S\$900,000 (≈ US\$632,000) - this was in the news because it broke a local (Clementi) record, but it doesn't get much cheaper than that.
There are some subsidies for first-time Singaporean home-buyers: If both you and your spouse are first-time buyers, then you get a total subsidy of S\$30,000. But this is not a large subsidy.
Some exceptional hardship cases (which involves an elaborate application process and onerous requirements) get to rent a small one-room flat for extremely cheap (as little as S\$26 a month), but these cases are so few in number as to be negligible.
- Public transport is not a perennial loss-maker, but rather a profit-maker!
Unlike in say some US cities, where public transport is always losing money, public transport in Singapore ALWAYS makes very healthy profits. So these are not drains on but rather contributors to the government coffers.
If you've only been in US cities where there's often only a few people on a bus, you may find it hard to imagine. But come to any Asian city where public transport is always jam-packed and you can see why public transport is so profitable.
This is a forced retirement savings scheme. In Sep 2015, the CPF had S\$293.9b in total members' balances (source). That's about 75% of GDP.
This is another frequent gripe of Singaporeans because these savings are all locked up (with very draconian rules on how you can gradually withdraw small amounts after you're 55).
Moreover, these funds are "managed" by the various Singapore sovereign wealth funds (GIC, Temasek). GIC in particular is not well-ranked in terms of transparency (source). So it is unclear as to how and how much exactly these help to contribute to Singapore government coffers.
- Health care is very efficient (at least if compared to say the USA)
Healthcare spending is 4.6% of GDP (World Bank).
I have heard some of my friends who work at the Ministry of Health (Singapore) complaining about how inefficient the Singapore health care system is.
But as someone who has lived in both Singapore and the US for a good number of years, I would say (based purely on my own anecdotal experience) that the Singapore healthcare system is extremely efficient, especially if compared to the US. But the US is perhaps the worst-case scenario. I'm not sure how Singapore would compare to other first-world countries.