The former. The Everything engine (upon which PerlMonks is based) is primarily code driven. At the page top level, Everything does use an ASP/JSP-like template format. But a typical template as used here consists of a bunch of calls to code and very little (often zero) HTML. For example, the Perl Monks Discussion page's template looks like this:

[{get_sitedoclet}]
[{votehead}]
[{newlistapproved:monkdiscuss,monkdiscuss approved linktype,PerlMonks 
+Discussions,15,navbaron,showunapproved}]
[{votefoot}]
[{newmoderatelist:monkdiscuss,monkdiscuss approved linktype,Unapproved
+ Discussions}]
[{addnewform:monkdiscuss,Discussion Item,Give us your input}]
[download]

Each one of those is a call to code. And yes, everything is stored in the database.*

* The exceptions are the scripts that actually handle the web request (index.pl) and the common modules, such as CGI.pm, and a few cron scripts, such as Vote Fairy.