How dressed up or not you get is totally up to you. At our table (second seating) on our last cruise we had 2 tuxes, a suit and an aloha shirt for the men, and the ladies opted for gowns, cocktail dresses, and a sundress. Elsewhere, I saw men in dress shirts, with and without a tie, and polo/golf shirts, with women tending more toward cocktail dresses, but with a sprinkling of gowns, pant suits, sparkly or silk tops, etc. We also had a few who wore shorts and even a few of those in t-shirts.
Most people seem to make an effort to dress nice, but only a small percentage dress formally, and women moreso than men. Most also seemed to shift back into more casual clothing after dinner (and all the photos were done).
For semi-formal night we saw much the same, though fewer coats for the men. I wear my tux both nights to justify the space and weight in my luggage. DW wears the same dress and shoes but different jewelry.