Avoiding is any action taken which is intended to get out of melee or otherwise avoid a combat situation. It is covered by action type A in the combat procedure.
Fleeing happens when an NPC or creature fails a morale check. Four possibilities for morale failure are listed on DMG 67, but they aren't mechanically explained. The following system is recommended for each of the four actions:
Move 1” in a direction away from the line of combat. This is controlled movement and keeps your face to the enemy. All enemies locked in melee with you can choose to either (1) let you disengage, (2) keep you engaged. If they choose to keep you engaged, they follow you (as “free” movement), and blows are struck normally on both sides. The falling-back party may of course choose to parry instead. In the case of NPCs and monsters, a leader might be able to rally troops who failed a morale check.
Give enemies in melee with you at the start of your action a free rear+stunned attack routine against you (+4, no shield, no dex modifier, allows backstab, does not stack with invisibility). After these attacks resolve, you move up to your full MV. Next round, the enemy party may opt to pursue, at which point the melee is ended and we go to pursuit rules. As with Option 1, NPC and monster troops may be rallied by a leader.
Works like Option 2, except it’s totally uncontrolled. For PCs, this option would never be selected since they aren’t subject to morale checks. PCs would only be fleeing in panic if the players decided to flee and then were confused as to what direction to go in, or there was otherwise general confusion at the actual gaming table, in which case the DM would interpret that as their PCs being uncoordinated. For NPCs and monsters, this option means that the fleers may go in separate or poor directions, drop items, and so on. Unlike Option 1 and Option 2, NPCs and monsters will not be able to be rallied. If the fleeing enemy is pursued or cornered, they may fight to the death (DM fiat).
If NPCs or monsters have reason to believe their surrender will not be accepted, they may instead take Option 3 (DM fiat). If NPCs or monsters surrender and their surrender is not accepted, they will switch to Option 3 on the following round. If PCs surrender, DM may call for a reaction check to determine how the surrender is received. If the enemy party is a type that takes slaves or prisoners, this is considered.