Counting Distinct Records

I am wondering whether the following two forms of SELECT statements are 
logically equivalent:

SELECT COUNT( DISTINCT table.column ) ...

and

SELECT DISTINCT COUNT( * ) ...

If they are the same, then why is the latter query much slower in 
postgres when applied to the same FROM and WHERE clauses?

Furthermore, is there a better way of performing this sort of operation 
in postgres (or just in SQL in general)?

Thanks!

-tfo

--
Thomas F. O'Connell
Co-Founder, Information Architect
Sitening, LLC
http://www.sitening.com/
110 30th Avenue North, Suite 6
Nashville, TN 37203-6320
615-260-0005