Healing can be confusing, thanks to the wording, so here we go.
Currently when you use first aid (as clarified by the Errata):
The character makes a test (for ALL damage from ALL sources) and the amount of health healed is applied to the character. Any remaining LOST wounds can NOT be healed using First Aid UNTIL they are healed using Natural Healing or other essoteric form of healing (call these wounds: Treated wounds). Any wounds successfully healed by First Aid may again be healed with First Aid later on without the need for Natural Healing.
Character A takes 5 wounds
Character B heals 3 wounds using First Aid
A still has 2 wounds of damage BUT these are Treated wounds now
A must naturally heal those 2 Treated wounds before they may be healed with First Aid again
Exceptions to the healing rules are (wound thresholds):
Heavily damaged characters only heal 1 wound from First Aid
Critically damaged characters only heal 1 wound from First Aid
Most healing characters have talents or abilities which MODIFY the wound thresholds. These include items like the Netharcium, which increases the Wound threshold for Heavily wounded to 3 X TB, but ONLY when using that item for First Aid. Normally a character with 5 TB and 12 wounds would be Heavily wounded once he drops to 2 remaining wounds. A character with a netharcium considers this character Lightly Wounded up to 3 points into critical when using First Aid. Therefore the character will heal the full amount as long as he is not 4 or more into critical damage. The character still Naturally heals as if critically damaged, and any character WITHOUT the special equipment still count the character as Heavy or Critically damaged.
For your example:
Let us assume your character in question has a TB of 8 and 20 wounds and the Apothecary has an Int score of 40.
Using a netharcium the apothacary treats the character's Lightly Wounded threshold as 24 (8 x 3). At 2 Critical, the character counts as having suffered 22 wounds and therefore the Apothecary counts the character as Lightly Wounded and can heal him as normal.
The apothecary makes a First Aid test and rolls a 52, which succeeds (netharcium adds +20 to Medicae tests on Space Marines: 40+20=60). The apothecary will heal 8 damage (Netharcium doubles wounds healed: Int Bonus x 2) and rolls a 3 for his additional 1d5 damage for a total of 11 wounds healed.
The character heals up to 9 wounds. The remaining 11 (Treated) missing wounds can NOT be healed by First Aid UNTIL they are healed using Natural Healing, although the 9 wounds and 2 crit wounds can be. Luckily for the Space Marine he is now only Lightly damaged and will heal 1 damage a day.