Clustering is grouping, like in an algebraic expression. Parentheses limit how far back and forward an alternator (vertical bar) applies:
/foo|bar/; # Matches "foo" or "bar"
/fo(o|b)ar/;# Matches "fooar" or "fobar"
Grouping also allows quantifiers to apply to more than one atom:
/foo{3}/ # Matches "foooo"
/(foo){3}/ # Matches "foofoofoo"
Capturing is storing the parenthesized portion of the match somewhere that you can refer back to it (as $1, or as an element of the list returned by a match, for example). Ordinary parentheses are capturing parentheses. Special parentheses (any that have a ? after the opening paren) are non-capturing. All parentheses group their contents.
We're not really tightening our belts, it just feels that way because we're getting fatter.