从Wikipedia中，如果它们的累积分布函数 (CDF) 对于域的任何元素都相同，则两个随机变量 (RV)（备注：您可以将其推广到任意数量的 RV）是独立且同分布的 (iid)$I$如果他们的联合 CDF 分解了边际 CDF 的乘积。这意味着：

$${\begin{aligned}&F_{X}(x)=F_{Y}(x)\,&\forall x\in I\\&F_{X,Y}(x,y)=F_{X}(x)\cdot F_{Y}(y)\,&\forall x,y\in I\end{aligned}}$$

(Note that this also imply that their pdfs are the same (almost everywhere, i.e. on the whole domain except for sets of measure zero, but this is a technical condition so don't worry about it)

Realizations of an RV are usually referred to as samples, i.e. roughly speaking their outcome. The assumption that samples generated by an RV are i.i.d. simply refers to the fact that underlying RVs, whose realizations you observe in the samples, are i.i.d.

So replying to your questions:

1. they are essentially the same thing.

2. You can regard it as repeated measurements of one random variable since the CDFs of two i.i.d. RVs are the same.