It is equivalent (usually, otherwise it would be explicitly stated).

The “star-operation” is called a Kleene-star, and it is an operation that basically takes the set and creats the set of all combinations of items from the original set. In the example of ${0,1}$, we would have that ${0,1}^*={0^{k_1}1^{k_2}0^{k_3}dotsmid k_1,k_2,dotsin mathbb{N}}$, and intuitively speaking, this is the set of all words created from the alphabet ${0,1}$. This obviously is also true for any other alphabet $Sigma$ you wod want.