1st attack mode is suggested for character classes that use more skills than others, such as Muse.
After targeting an enemy by clicking the left mouse button, you can choose a skill to attack.
Double clicking the left button of a mouse will initiate attacks.

2nd attack mode is convenient for characters that use fewer skills and more physical attacks.
A single left click of the mouse will both target an enemy and initiate attack at the same time,
so the 2nd attack mode is easier for melee class characters to hunt monsters.