#!/usr/bin/perl

# create names lookup table from first file
while (<>) {
    $names{$_} = 1;
    last if eof;
}

$/ = "\n>";  # set input record separator

# scan second file
while (<>) {
    print if /^>?(\w+\n)/ && $names{$1};
}

##</code><code>##

$ ./extract.pl file1 file2 >output

##</code><code>##

$ perl -ne'$/eq"\n"?$nm{$_}++:/^>?(\w+\n)/&&$nm{$1}&&print;$/="\n>"if eof' file1 file2 >output

##</code><code>##

$ perl -ne'1..eof&&($/=">")?${$_}++:/.+\n/&${$&}&&print' file1 file2 >output