Running rigging is a general term that is given to all the moving lines or ropes that operate the sails and yards, there is nearly 200 of them on the ship and they all have a specific name and function. 

The BRACE LINES change the angle of the yards.

The CLEWLINES, BUNTLINES, LEECHLINES, SHEETS, HALLIARDS and DOWNHAULS are used to operate the SQUARE SAILS.

HALLIARDS, SHEETS and DOWNHAULS are used to operate the FORE AND AFT SAILS.