What is the difference between a unit trust and a mutual fund?

Same same. Different countries call them different things.

I've only actually heard the term Unit Trust in Singapore.

Other countries like US, UK, India, Philippines, all call them Mutual Funds.

A unit trust fund pools money from investors to meet a specific financial objective. The manager of the fund then takes the money and invest it in various shares or bond. A mutual fund is similar to a unit trust however differing factor is the legal structure. A mutual fund issues redeemable shares while a unit trust can only issue units as it is not an investment company.