What are the white and yellow numbers seen during combat?

While firing at the enemies you see both white and yellow 'scores' flying about.

What are they - and whats the difference between white and yellow?

The numbers indicate how much damage you deal to the mob.

It will have a color that indicates the "type" of damage, and this includes various categories, let me summarize them along with some references.

• Gray - Damage is reduced

  When you're significantly higher level than the mobs/area, your damage is scaled down so that you still need to fight the mobs and not just oneshot them. This is done to increase replayability, and to make it possible for a high-level player to play with a low-level player without effectively just being able to sneeze to kill everything in the zone.

• White - Normal kinetic damage

  Most of your damage from your weapons will be this damage.

• Yellow - Critical hits

  Mostly gotten when you fire on the critical spots on an enemy, like heads on most humanoids and the bellies on some of the Vex. Some enemies doesn't have a critical spot, like the Shanks. Note that you can get critical hits also when firing on other parts of the enemy, but you significantly increase the chance of getting one if you fire on the critical spots.

• Blue - Arcane elemental damage (see note below)

  Dealt by Arcane weapons when fired on Arcane (blue) shields. The Arcane elemental has a blue "razor"-like icon on the weapon.

• Orange - Solar elemental damage (see note below)

  Dealt by Solar weapons when fired on Solar (orange) shields. The Solar elemental has an orange flame icon on the weapon.

• Purple - Void elemental damage (see note below)

  Dealt by Void weapons when fired on Void (purple) shields. The Void elemental has a purple spiral icon on the weapon.

Note that elemental weapons does normal white or yellow or gray damage when fired on a mob that doesn't have a shield (either because it never had a shield, or you have already removed it). The elemental part of the damage only comes into play when fired upon the corresponding shield type.

There are several possible colors that may show up when damaging an enemy.

• White is the most common color, which indicates normal kinetic damage.
• Yellow indicates critical hits, which is often shown when shooting the critical spot of an enemy (Some enemies doesn't have this critical hit spot, like Fallen Shanks). Usually this is in the head of the enemy.
• Grey indicates "weak damage", which appears when you are significantly higher level than your enemy, you deal reduced damage. This is a mean of balancing the game for higher/lower leveled players/enemies.
• There's also the colors blue, orange/red, and purple, which indicates which elemental damage you inflict to the enemy. This is only effective when shooting the matching shield of an enemy.