Edited for clarity
According to the SQL Specification, a primary key can not contain NULL. This means that decorating a column with either "NOT NULL PRIMARY KEY" or just "PRIMARY KEY" should do the same thing. But you are relying on the SQL engine in question correctly following the SQL standard. As an example due to an early bug, SQL Lite does not correctly implement the standard and allows null values in non-integer primary keys (see sqlite.org/lang_createtable.html). That would mean for (atleast) SQLLite the two statements do two different things.
As "NOT NULL PRIMARY KEY" clearly indicates intent and continues to enfore non-null values even if the primary key is removed, that should be the prefered syntax.