Difference between GROUP_CONCAT() and CONCAT_WS()?

I have searched unsuccessfully for a satisfactory explanation on the difference between GROUP_CONCAT() and CONCAT_WS().

GROUP_CONCAT is used when you want to have non-NULL values from different column rows in a single row. For this you need to have GROUP BY to work.

CONCAT_WS is to join two or more strings.

Example

GROUP_CONCAT(CONCAT_WS(' ', firstname, lastname) ORDER BY id ASC SEPARATOR ',');

Outputs something like,

John Doe,Blah Blah,Tom Cruise,Lorem Ipsum

here space between the name is because of CONCAT_WS, while whole result in one row is because of GROUP_CONCAT