I'd apply two s/// conditionally. Assuming that the words going into section or h1 tags are all on a line:

while(<DATA>) {
    s!(?<=<sb>)<s(\d+)>(.*)!<h$1>$2</h$1>!
      or
        s!<s(\d+)>(.*)!<section$1>$2</section$1>!;
    print
}
__DATA__
<s1>King of England
JAMES, by the Grace of God, King of England, Scotland, France and Irel
+and, Defender of the Faith...
...
This first selection was written in England to establish the colony of
+ Virginia
<sb><s1>Rights of Landowners
We, greatly commending, and graciously accepting of, their Desires for
+ the Furtherance</sb>
[download]

outputs

<section1>King of England</section1>
JAMES, by the Grace of God, King of England, Scotland, France and Irel
+and, Defender of the Faith...
...
This first selection was written in England to establish the colony of
+ Virginia
<sb><h1>Rights of Landowners</h1>
We, greatly commending, and graciously accepting of, their Desires for
+ the Furtherance</sb>
[download]

_($_=" "x(1<<5)."?\n".q·/)Oo.  G°\        /
                              /\_¯/(q    /
----------------------------  \__(m.====·.(_("always off the crowd"))."·
");sub _{s./.($e="'Itrs `mnsgdq Gdbj O`qkdq")=~y/"-y/#-z/;$e.e && print}