It doesn't unless variable interpolation is involved (s/// is like "", but s''' is like ""), but your regexes aren't equivalent(you fixed typo).

D:\>perl
$bar = 1; $_ = 123;  s/$bar/bar said $bar -/; print
__END__
bar said 1 -23
D:\>
D:\>
D:\>perl
$bar = 1; $_ = 123; s'$bar'bar said $bar -'; print
__END__
123
D:\>perl
$bar = 1; $_ = 123; s'1'bar said $bar -'; print
__END__
bar said $bar -23
D:\>
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To see if the shell does interpolation, use B::Deparse, ex perl -MO=Deparse ...