This would depend slightly by jurisdiction, so I'll try to give you an answer using the Model Penal Code. The MPC has been adopted, either in part or in full, by most states. If your scenario doesn't happen in the United States, then just ignore everything I say.

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Assault

The Model Penal Code (MPC) § 211.1 separates assault into two general categories: simple assault and aggravated assault:

(1) Simple assault: a person is guilty of simple assault if he: (a) attempts to cause or purposely, knowingly or recklessly causes bodily injury to another; or (b) negligently causes bodily injury to another with a deadly weapon; or (c) attempts by physical menace to put another in fear of imminent serious bodily injury.

(2) Aggravated assault: a person is guilty of aggravated assault if he:
(a) attempts to cause serious bodily injury to another, or causes such injury purposely, knowingly or recklessly under circumstances manifesting extreme indifference to the value of human life; or (b) attempts to cause or purposely or knowingly causes bodily injury to another with a deadly weapon.

Source.

Manslaughter

Under the Model Penal Code section 210.3, voluntary manslaughter is homicide which would otherwise be murder that is committed under the influence of extreme mental or emotional disturbance for which there is reasonable explanation or excuse. The Code uses a reasonable person standard to determine the validity of the alleged explanation or excuse.

The Model Penal Code defines involuntary manslaughter when an individual commits criminal homicide in a reckless manner. Criminal homicide is a broad concept: the Code states that an individual commits criminal homicide when a person "purposely, knowingly, recklessly or negligently causes the death of another human being."

Source-1. Source-2.

Murder

Under the Model Penal Code, the following constitute murder:

Purposefully or knowingly killing another human being. This functions much the same as the common law rule against intentional murder.

Killing another human being in circumstances showing extreme recklessness. This functions much the same as the common law's depraved heart murder rule.

Felony-murder. The Model Penal Code disfavors but does not eliminate applying the death penalty for killings that occur during the commission of a felony. Instead of framing the rule as a felony-murder rule, it creates a rebuttable presumption that killings which occur during the commission of listed dangerous felonies show extreme recklessness for purposes of the code's other murder provisions.

Given your scenario of:

• A assaults C w/o fatal wounds.
• Later, B assaults C w/ fatal wounds.

Your questions:

• Person A had the intent to kill, or didn't.
  • Assault:
    • A will be charged with assault, as long as one of the elements of assault (above) is met.
    • B will not be charged for assault, but instead for murder because murder includes the lesser included offense of assault. You can't murder someone without having assaulted them first. This is known as the merger doctrine.
  • Manslaughter:
    • A will not be charged with manslaughter, because he wasn't the one to cause the fatal wound.
    • B could be charged with manslaughter if it fits one of the elements of manslaughter.
• Person A knew Person B personally, or didn't.
  • Doesn't matter.
• The timeframe between both incidents was either 5 seconds, 5 minutes, or 1 day.
  • Might matter for manslaughter. Doesn't matter for assault or murder.

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