Strictly speaking, a 'mac' should be made of a rubberised material. However, the term is now used generically to describe any form of raincoat.
'Trench coat' should (in theory) describe the style of raincoat used by the army:
http://en.wikipedia.org/wiki/Trench_coat
In practice, there's no clear division between the two. The same style could be called a 'mac' by one person and a 'trench coat' by another. However, it's more likely that your granny would choose to call it a 'mac' (and buy it from a discount store), while your well-healed friend with a villa, a Lamborghini and a yacht would call it a 'trench coat' (and buy it from a designer boutique).
However, in some cases, 'trench coat' can be associated with quite heavy garments. So you're either looking for a 'mac' or a 'light-weight trench coat'.
Personally, I wouldn't bother trying to differentiate between the two. I'd simply walk into a shop and say that I'd like to buy a raincoat. I'd then buy the one I liked best, irrespective of whether the label said it was a 'mac' or a 'trench coat'.
Chris