You're correct in thinking they are (almost) the same thing, but it's easier for average people (including people starting out in statistics) to think of "fair dice", "fair coin", "roulette wheel" or "what are the chances Ms Johnson has two boys..." versus something like "the discrete uniform distribution of {1, 2, 3, 4, 5, 6}" or "assume an independent binary process repeated 3 times..." or whatever.

So, why "(almost)"? Because, in the real world, there are no fair die, no fair coins (I believe a study recently showed that the way most people flip coins, the side that was up originally is more likely to be up after the flip), gender distribution at birth is unequal (more boys born than girls), and so on. There isn't even really such a thing as a random sample since we have no way to generate true randomness.

So, the whole coin/marbles/roulette wheel/etc thing is just a way to make statistics more accessible to the beginners and the average person