This demonstrates the (a?) difference. How you interprete the results relative to the descriptions I can't quite figure.

 perl> $s = join'','a'..'z'

 perl> 1 while $s =~ m[((.).)(?{ print "$^N:$+\n"; })]g
ab:a
cd:c
ef:e
gh:g
ij:i
kl:k
mn:m
op:o
qr:q
st:s
uv:u
wx:w
yz:y


 perl> 1 while $s =~ m[((..).)(?{ print "$^N:$+\n"; })]g
abc:ab
def:de
ghi:gh
jkl:jk
mno:mn
pqr:pq
stu:st
vwx:vw
[download]

One interesting difference in the description that had me salivating breifly was that $+ is explicity defined read-only whereas (in your snippet) $^N it's not but whilst attempting to assign to it doesn't result in an error, it also has no effect on the bound string.