In 5e, with few exceptions, this is left to the DM
Combat Step by Step on page 189, PHB states:
- Determine surprise. The DM determines whether anyone
involved in the combat encounter is surprised.
- Establish positions. The DM decides where all the
characters and monsters are located. Given the
adventurers’ marching order or their stated positions in
the room or other location, the DM figures out where the
adversaries are—how far away and in what direction.
So this is explictly left to the DM, with little further guidance. For Underwater Encounters, the DMG provides an an encounter distance table on p. 116:
|Creature Size [sic]
|Clear water, bright light
|Clear water, dim light
|Murky water or no light
For sea travel, it offers the following (p. 119)
A relatively calm sea offers great visibility. From a
crow's nest, a lookout can spot another ship or a
coastline up to 10 miles away, assuming clear skies.
Overcast skies reduce that distance by half. Rain and
fog reduce visibility just as they do on land.
On the Ethereal plane, visibility is limited (p. 48 DMG):
Visibility in the Border Ethereal is limited to 60 feet. The plane's depths comprise a region of swirling mist and fog called the Deep Ethereal, where visibility is limited to 30 feet.
In closed environments or darkness it may be relatively easy -- line of sight or darkvision limit how far you can see, at least, and can form a natural baseline. The DMG covers Noticing Other Creatures on page 243, and bases this on skill checks, but does not provide distances by terrain:
While exploring, characters might encounter other
creatures. An important question in such a situation is
who notices whom.
Indoors, whether the sides can see one another
usually depends on the configuration of rooms and
passageways. Vision might also be limited by light
sources. Outdoor visibility can be hampered by terrain,
weather, and time of day. Creatures can be more likely
to hear one another before they see anything.
If neither side is being stealthy, creatures
automatically notice each other once they are within
sight or hearing range of one another. Otherwise,
compare the Dexterity (Stealth) check results of the
creatures in the group that is hiding with the passive
Wisdom (Perception) scores of the other group, as
explained in the Player's Handbook.
In Tomb of Annihilation, you get visibility in heavy rain (p.11):
Visibility in heavy rain is limited to 50 yards. Beyond
that distance, only Huge or larger objects can be distinguished. Missile weapon ranges are halved during rain.
In Wild Beyond the Witchlight you get visibility in thick fog (p. 74):
Thick fog hangs over all outdoor areas, limiting visibility to 20 feet.
In Icewind Dale: Rime of the Frostmaiden, you get blizzards (p. 10) [Thank you to Pepijn]:
A blizzard's howling wind limits hearing to a range of 100 feet (...) It also imposes disadvantage on Wisdom (Perception) checks that rely on hearing. Visibility in a blizzard is reduced to 30 feet.
Real world limits to visibility
Lastly, 200 feet in grassland is not a large distance to see someone at. The human eye can see things that are miles away if there are no obstructions, and you can see the light of stars that are thousansds and galaxies that are even millions of light years away. On a planet comparable in size to the earth (such as Toril of the Forgotten Realms), you would be limited primarily by the surfaces curvature, and be able to see about 3 miles on flat terrain, and much further if you are higher up on a tower, mast or mountain.
What is mostly limiting seeing distance in the open in addition to this is the atmosphre (air scattering light, fog, rain etc.), things in the way (trees, hills, mountains, houses etc.), light conditions (twilight, darkness), and how big or small the things you aim to see are (small detail being lost in distance). The many combinations of realistically combining these is likely why the DMG does not aim to codify it as a rule.
The relatively short sighting distance on the DMG screen for terrain of only 6d6 x 10 (average 210) feet in terrain like desert or grassland helps playablitiy: they allow ranged combat for just a few rounds and in a range where longer-ranged weapons have reach. But realistically, you would see another group at a larger distance than that in the open, if they were not hiding or lying in ambush.