What's the difference between $a^*+b^*$ and $(a+b)^*$?
$a^*+b^*$ generates words that either consist of any amount of $a$s or any amount of $b$s, like: $a$, $aaaaa$, $bbbb$
$(a+b)^*$ generates secquences of either $a$ or $b$, for example: $abab$, $aabb$, $bbaa$,...


So, the main difference is, that in 1 you either get strings only containing as or only containing bs. Regex 2 produces a language where you have no order of characters and can put both in.

So, both don't produce the same language, but 1 is a subset of 2.