The intents of the different kinds of tests aren't at all Perl-specific, so you could try looking at the definitions of these terms on some other sites.

For example, at C2, compare Unit Test aka Programmer Test against Acceptance Test aka Customer Test.

You can write both unit tests and acceptance tests using the standard Perl Test::* modules.

There are also several testing modules that are derived from the XP-style unit testing frameworks used in other languages; you may find these are helpful ways to structure your test code, but there's no requirement that you use them. A quick search found Test::Unit, Test::SimpleUnit, Test::Class, Test::Extreme, and I'm sure there are others.