Which is the correct rules text for Darkvision?
Reading the PHB sections on races, e.g. Dwarf p. 20, it says ...
Darkvision. Accustomed to life underground, you have superior vision in dark and dim conditions. You can see in dim light within 60 feet of you as if it were bright light, and in darkness as if it were dim light. You can't discern color in darkness, only shades of gray.
But at PHB p.184 it doesn't mention dim lighting conditions, only what Darkvision does in full darkness. It says ...
Darkvision: Many creatures in the worlds of D&D, especially those that dwell underground, have darkvision. Within a specified range, a creature with darkvision can see in darkness as if the darkness were dim light, so areas of darkness are only lightly obscured as far as that creature is concerned. However, the creature can't discern color in darkness, only shades of gray.
So the various character races can see in darkness as if it were dim, and in dim light as if it were bright, whereas "creatures" can only see in darkness as if it were dim?
Interesting point regarding the description of darkvision on PHB p. 184. However, the Monster Manual on p. 9 says:
A monster with darkvision can see in the dark within a specific radius. The monster can see in dim light within the radius as if it were bright light, and in darkness as if it were dim light. The monster can't discern color in darkness, only shades of gray. Many creatures that live underground have this special sense.
This definition matches the PHB definition on p. 20. Comparing the PHB p. 20 and MM p. 9 definitions on the one hand with the PHB p. 184 definitions on the other, the only part in discrepancy is the part about "see in dim light within the radius as if it were bright light." The omission from p. 184 is only that, an omission. It isn't a contradiction.
It's reasonable to conclude that by RAW darkvision is darkvision, and works the same for every creature, unless otherwise noted in the creature's description.
The description on PHB p. 184-185 was corrected in this errata, which says:
Darkvision (p. 185). The definition of darkvision here now matches the definition everywhere else in the game (6th printing).
In summary, the definition of darkvision listed on p. 20 of the PHB is correct, and the omission on p. 185 was corrected in errata.