difference b/w [ab] and (a|b) in regex match?

I knew that [] denotes a set of allowable characters -

>>> p = r'^[ab]$'
>>> 
>>> re.search(p, '')
>>> re.search(p, 'a')
<_sre.SRE_Match object at 0x1004823d8>
>>> re.search(p, 'b')
<_sre.SRE_Match object at 0x100482370>
>>> re.search(p, 'ab')
>>> re.search(p, 'ba')

But ... today I came across an expression with vertical bars within parenthesis to define mutually exclusive patterns -

>>> q = r'^(a|b)$'
>>> 
>>> re.search(q, '')
>>> re.search(q, 'a')
<_sre.SRE_Match object at 0x100498dc8>
>>> re.search(q, 'b')
<_sre.SRE_Match object at 0x100498e40>
>>> re.search(q, 'ab')
>>> re.search(q, 'ba')

This seems to mimic the same functionality as above, or am I missing something?

PS: In Python parenthesis themselves are used to define logical groups of matched text. If I use the second technique, then how do I use parenthesis for both jobs?