Nah. They both mean pretty much the same thing, except a "flat" is generally in a multi-storey complex and a "unit" is town-house type affair. But a flat can also be a separate building on the same block as a larger house, like a granny flat or a converted garage or caravan. Maybe you should start asking to see "apartments" and really throw a spanner in the works.
Yeah the reason I asked was because I entered two contracts in a street I know... know these blocks are completely identical but one was listed as a flat and the other as a unit... it made me scratch my head!
They're essentially the same thing, although strangely I would be more open to viewing a 'flat' than a 'unit' 'Unit' makes me think of holiday accommodation.