Smart casual vs semi-formal
Here is what I understand by the following terms.
Formal daytime - morning wear (i.e. frock coat)
Formal evening - white tie and tail
Semi-formal day - Suit (dark coloured, BLACK polished shoes, needles to say tie)
Semi-formal evening - dinner jacket (or tuxedo as Americans call them) the DJ can be white in summer time
Smart-casual - blazer / jacket and tie, trousers (NOT jeans)
The invite is wrong you can't suggest wearing either a DJ or smart casual.