If by "normal regex" you mean Perl-Compatible Regular Expressions (PCRE), then the Vim help provides a good summary of the differences between Vim's regexes and Perl's:
:help perl-patterns
Here's what it says as of Vim 7.2:
9. Compare with Perl patterns *perl-patterns*
Vim's regexes are most similar to Perl's, in terms of what you can do. The
difference between them is mostly just notation; here's a summary of where
they differ:
Capability in Vimspeak in Perlspeak ~
----------------------------------------------------------------
force case insensitivity c (?i)
force case sensitivity C (?-i)
backref-less grouping \%(atom) (?:atom)
conservative quantifiers {-n,m} *?, +?, ??, {}?
0-width match atom@= (?=atom)
0-width non-match atom@! (?!atom)
0-width preceding match atom@<= (?<=atom)
0-width preceding non-match atom@<! (?!atom)
match without retry atom@> (?>atom)
Vim and Perl handle newline characters inside a string a bit differently:
In Perl, ^ and $ only match at the very beginning and end of the text,
by default, but you can set the 'm' flag, which lets them match at
embedded newlines as well. You can also set the 's' flag, which causes
a . to match newlines as well. (Both these flags can be changed inside
a pattern using the same syntax used for the i flag above, BTW.)
On the other hand, Vim's ^ and $ always match at embedded newlines, and
you get two separate atoms, \%^ and \%$, which only match at the very
start and end of the text, respectively. Vim solves the second problem
by giving you the \_ "modifier": put it in front of a . or a character
class, and they will match newlines as well.
Finally, these constructs are unique to Perl:
- execution of arbitrary code in the regex: (?{perl code})
- conditional expressions: (?(condition)true-expr|false-expr)
...and these are unique to Vim:
- changing the magic-ness of a pattern: v V m M
(very useful for avoiding backslashitis)
- sequence of optionally matching atoms: \%[atoms]
- & (which is to | what "and" is to "or"; it forces several branches
to match at one spot)
- matching lines/columns by number: \%5l \%5c \%5v
- setting the start and end of the match: zs ze
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