What's the difference between scam and fraud?

The biggest difference between the two words is that fraud has a long history in English and a well-established status in English and U.S. law, whereas scam goes back—according to Merriam-Webster's Eleventh Collegiate Dictionary (2003)—only to 1963, is of unknown origin, and clearly entered the language as a slang word, meaning that it was initially ill-defined and very informal.

Black's Law Dictionary, revised fourth edition (1968) devotes considerable space (almost two full pages) to legal definitions of fraud and of its various special forms (fraud in treaty, fraudulent alienation, fraudulent concealment, fraudulent conversion, fraudulent conveyance, fraudulent preferences, and fraudulent representation). At its most basic level, fraud has received the various judicial definitions included in this entry from Black's:

FRAUD. An intentional perversion of truth for the purpose of inducing another in reliance upon it to part with some valuable thing belonging to him or to surrender a legal right; a false representation of a matter of fact, whether by words or by conduct, by false or misleading allegations, or by concealment of that which should have been disclosed, which deceives and is intended to deceive another so that he shall act upon it to his legal injury. [Citation omitted.] Any kind of artifice employed by one person to deceive another. [Citation omitted.] A generic term, embracing all multifarious means which human ingenuity can devise, and which are resorted to by one individual to get advantage over another by false suggestions or by suppression of truth, and includes all surprise, trick, cunning, dissembling, and any unfair way by which another is cheated. [Citation omitted.] "Bad faith" and "fraud" are synonymous, and also synonyms of dishonesty, infidelity, faithlessness, perfidy, unfairness, etc. [Citation omitted.]

The particular definitions of different categories of frauds are defined in the statutes or ordinances of the relevant governing body of a given jurisdiction. The point of the definitions there is to establish grounds for criminal liability for anyone who engages in the proscribed conduct.

Here, in stark contrast, is the definition of scam in Robert Chapman & Barbara Kipfer, Dictionary of American Slang, third edition (1995):

scam 1 n (also scambo) by 1963 A swindle, confidence game; fraud; =CON. It was a full scam—Time/Looking for a good scambo for April Fool's Day...—Milwaukee Journal 2 v (also scam on) : You guys are scamming me—Joseph Wambaugh 3 n by 1964 The information; =the LOWDOWN, the SCOOP: Here's the scam... We're holing in for the night—Patrick Mann {origin unknown; perhaps related to early 1800s British scamp, "cheater, swindler"}

In short, scam has no legal status as a term of law in most jurisdictions, except insofar as it may be defined as a type of fraud. The term fraud is broad but usually very carefully defined in statutory law. Signing a deceptive contract that leads one to lose lots of money may well fall within the definition of fraud in many places—although the trick is to prove that the contract is truly deceptive and not merely disadvantageous after the fact to the signer.

They are synonyms but have a subtle difference. A scam almost always involves money or transactions that involve monetary loss to the victim. But on the other hand, fraud is a broader term which might involve money or other gains or even bringing disrepute to a person.

According to this source,

Fraud is a broader category of wrongdoing than a scam. Scams can belong to the broader category of fraud.

A scam is generally a more minor offense than fraud, which is considered very serious.

In your example, the scammers (people who scam others) have come up with a deceptive contractual agreement. The victim would've signed without reading the entire document, eventually finding out that they have been cheated.

An example of fraud would be someone trying to impersonate you in an exam or submitting forged documents to gain entry into another country, etc.

As a matter of English usage, the main difference is that scam is more accepted as a countable noun - there's "scams", or "a scam" (referring either to a particular incident or a particular method of committing fraud), whereas such usage is not as accepted with the word "fraud" in many dialects of English. This would account for the differences you've seen in reference to the particular incidents you are asking about.

It's hard to find citations showing this - dictionaries tend to simply say "uncountable, countable" without any discussion of how common or accepted each usage is (The sole example it gives of a countable usage, "a $100 million fraud", sounds awkward to me).

There are some good answers here that describe the difference between a scam and a fraud. As to why this particular instance is generally called a scam rather than a fraud:

Your suspicion that it might have something to do with avoiding libel claims is plausible. In the US, the Constitutional protections for freedom of speech and freedom of the press in the 1st Amendment provide quite a bit of protection for defendants (see this article, among many possible sources, for more info). However, plaintiffs might well have an easier time in a jurisdiction without these considerations, like Singapore, and the slight difference in definition might matter there.

However, I think even in the US that "Sim Lim Scam" would be more attractive to copywriters than "Sim Lim Fraud". This is not due to any legal or definitional consideration, but purely to the sound of the words. Specifically, Sim Lim Scam has the dual attractions of being alliterative and consonant. Alliteration and consonance are both poetic or literary devices:

alliteration

the repetition of usually initial consonant sounds in two or more neighboring words or syllables (as wild and woolly, threatening throngs) (Merriam-Webster)

consonance

recurrence or repetition of consonants especially at the end of stressed syllables without the similar correspondence of vowels (as in the final sounds of “stroke” and “luck”) (Merriam-Webster, definition 2.a)

So Sim Lim Scam. This is the type of tuneful title¹ that can take root and sell copy.

¹ Doesn't that sound catchier than musical headline, even though individually the second set of words might make more sense?