For the union of sets we use the union operator $\cup$ (or $\bigcup$). And for a concatenation (Kleene star) we also use the union operator. The operations are different, but why the same terminology and operator?
The following is my understanding of the union of sets versus the concatenation of sets (Kleene star). Please correct me if I'm wrong.
Union of sets
For the two sets $\{a,b\}$ and $\{a,b\}$ we have the union \begin{align} \{a,b\}\cup\{a,b\}=\{a,b\} \tag 1 \end{align} Update: For reference I used Union (set theory) from Wikipedia.
Concatenation of sets (Kleene star)
The concatenation of $\{a,b\}$ and $\{a,b\}$ is also a union (same notation?!) of two sets \begin{align} \{a,b\}^*&=\bigcup _{i=0}^{2} \{a,b\} ^2 \tag 2\\ &=\{a,b\} \cup \{a,b\} \tag 3\\ &=\{\epsilon,a,b,aa,ab,ba,bb,aaa,aab,aba,abb,baa,\dots\} \tag 4 \end{align}
Update: For reference I used Kleene star from Wikipedia. And here's where my confusion lies because at Wikipedia they also use the notation with the union operator: $$ V^* = \bigcup_{i\geq 0} V^i = V^0\cup V^1 \cup V^2 \cup V^3 \cup V^4 \cup \cdots \tag 4 $$ Which is the same (?!) notation as in my $(2) - (3)$ but with the upper bound $2$. And the notation does not coincide with $(1)$.