Mutual Fund is more a USA term while Unit Trust is a UK term.
Instinctly implied, Mutual Fund is just a pool of collected investment money. The money is usually pooled for a specific purpose. Its also implied some special people are 'in charge' of the pool of money to achieve the purpose.
Unit is a special measurement method when there are more than one type of items to refer to; And yet one needs to use ONE system to measure all the items. So generally instead of gram, meter etc. 'Unit' is used instead. Trust instinctly implied confidence and someone who we can rely on. So Unit Trust is basically a 'system' you can rely on while it may consist of multiple elements in it. Despite its potential complexity, it should be easily understood by using its 'unit'.
As you may see by comparison now, Mutual Fund does not necessary have to have the Trust element in it. Unit Trust on the other hand, doesn't have to have more than 1 investor. In short, I can pool up all my friend's money and invest for them as a mutual fund. Nonetheless an illegal one because such activity require licenses in most part of the world. On the other hand, I can use part of my wealth to set up a unit trust to earn money from Melbourne real estates.
A little more than just layman talks
Trust is also a finance term where a 3rd party is brought into the transaction between 2 persons, acting as a balance entity fullfilling the interest for all. For example, Sandy has a oil mill that she wants to pass down to Benny but Benny doesn't know anything about it. So Sandy passes the ownership to Tan with the agreement that Tan will manage the whole operation but pass all the benefits to Benny.
Sandy is usually caleed the Settlor
Tan is Trustee
Benny is the Beneficiary
Usually Tan will charge a service fee and usually only large and stable finance institution can be considered as the real Trustee.
There are also some sayings that Unit Trust is part of Mutual Fund because Unit Trust is basically a Mutual Fund that has an extra element of Trust in it. The reason why both of these terms are used interchangeably is because all legitime Mutual Funds must setup a Trust in Malaysia. Which mean the fund company can manage the money but can NEVER take the money to their own possession as its own by the Trustee, not them. That way, the investors' money is safeguarded.
Frequently the corporate finance guys may also refer Mutual Fund and Unit Trust as Open End Fund. Which basically means investors buy and sell directly with the Fund Manager without the need to worry about other investors.