Sampling and averaging in Monte Carlo Simulation

Question

(First of all, I apologize for the vague title. Couldn't think of rather proper one.)

Let's say that we have 10 items where each item has probability distribution of one's own, say Lognormal distributions. In this case, I would like to know,

1. Are there differences between

   (i) when each item is sampled for, say 1000 times, and we choose the lowest value among 10 items.

   And

   (ii) when each item is sampled for once, and we choose the lowest value among 10 items. Then, we average these values over 1000 trials.

2. If there are differences, do each of the above have special meaning in probability study?

Any help would be appreciated.