Aspell Author Here.
Since Aspell 0.50, Pspell is no longer used. It is not necessary to download and install the Pspell package, only Aspell 0.50 (or better) is required. Aspell now provided a backwards compatibility interface for programs expecting the old Pspell interface (such as PHP).
Even though Aspell now provided a new "Aspell" interface this, the PHP Pspell interface is the one you want to use. The Aspell PHP interface is the one used with a *very* old version of Aspell as the manual says.
Sorry if this is confusing, but it is not really my fought as I have no control over PHP development. Eventually a new Aspell interface should be provided for PHP which uses the new Aspell interface provided with Aspell 0.50 but for now the Pspell interface will work just fine.
Note: If you wish to use an older version of Aspell (_before_ 0.50) than both Aspell and Pspell are required.