What do the different colored damage numbers represent?

As you have guessed, green numbers are healing.

Red numbers are standard damage.

Yellow numbers are the damage dealt when your character scores a critical hit.

White numbers I initially thought to be ability- or status-based damage, but after some more testing I believe it may be non-critical damage that ignores armour, such as statuses or abilities that specifically take a percentage of health, or Darth Sidious' Deathstroke ability (but only some of the time as it has a 25% chance to ignore armour).

Blue numbers are special damage (but not critical special damage, critical special damage is yellow). Special damage is dealt by attacks that specifically say they deal special damage, such as Talia's Harrowing Assault, or the Jedi Consular's Attack as Defense.

White Damage is unmitigated damage. This means it cannot be resisted/evaded and is unable to crit.

All White Damage attacks ignore armour by default. Some White attacks ignore armour/protection, but not all white attacks ignore protection, only armour.

Examples of effects/attacks that deal unmitigated damage:

• Deathmarked Characters take damage equal to 50% of the character's total health as unmitigated damage from all attacks in addition to regular damage.
• Damage over Time deals 5% of a character's total HP as unmitigated damage.
• Darth Nihilus's Annihilate ability does unmitigated damage to raid bosses (99,999 damage).
• Savage Opress's overpower ability does 99,999 unmitigated damage against enemies with less than 25% health (50% with Omega).
• Slave 1's Seismic Charge attack deals direct damage to Health, ignoring Armour/Protection, as well as taking 20/30% of the target's total health.
• The AAT's main cannon deals 99,999 unmitigated damage to characters without a buff.
• The Phase 4 Firestorm attack in Heroic AAT deal 99,999 unmitigated damage to all un-buffed characters.