SQL `count(1)` vs `count(*)` vs `count(id)`: only `count(id)` does not count `NULL` rows

sql-counts.sql

CREATE TABLE categories ( id integer );

CREATE TABLE products ( id integer, cat_id integer );

INSERT INTO categories(id) VALUES(1);
INSERT INTO categories(id) VALUES(2);

INSERT INTO products(id, cat_id) VALUES(1, 1);

SELECT c.id, count(1) FROM categories c
  LEFT JOIN products p
  ON c.id = p.cat_id
  GROUP BY c.id;

-- id	count
-- 1	1
-- 2	1
  
SELECT c.id, count(*) FROM categories c
  LEFT JOIN products p
  ON c.id = p.cat_id
  GROUP BY c.id;

-- id	count
-- 1	1
-- 2	1
  
SELECT c.id, count(p.id) FROM categories c
  LEFT JOIN products p
  ON c.id = p.cat_id
  GROUP BY c.id;

-- id	count
-- 1	1
-- 2	0
  
-- See http://sqlfiddle.com/#!9/c10c25/5/0