What's the difference between the concatenation and union of symbols within a language
Simply put,

the kleene star of concatenation gives
$$(ab)^* = \{\epsilon, ab, abab, ababab, ...\} $$

while the kleene star of union gives
$$(a+b)^* =\{\epsilon,a,b,aa,ab,ba,bb,\ldots\}$$

so you got it correctly, and indeed all the words you write belong to the language.



Recall that for any two sets $L,K$ we have
$LK = \{xy \mid x\in L, y\in K\}$,
$L+K = L \cup K$,
$L^* = \{\epsilon\} \cup L \cup L^2 \cdots$.

and recall that the regular expression "a" corresponds to the set $\{a\}$ and operations between regular expressions correspond to the above operations on sets.