With the new update, we now have "Sightings." However, there is no indication of how this differs from "nearby Pokémon", though in the patch notes, it states they are testing a variation of "Nearby Pokémon" which appears to be the "Sightings." How do "Sightings" differ from "Nearby Pokémon"?
The nearby system was originally supposed to show you pokemon spawns in order of distance (Which we all know didn't work at all). Essentially Sightings is now a list of what pokemon are currently in the area as opposed to listing every nearby spawn as an individual pokemon, which also caused a bunch of duplicates to clutter the tab. They also took out the ability to "watch" a pokemon since that was based on distance as well. Sightings doesn't appear to sort pokemon in any particular order, at least not alphabetically or numerically based on pokedex number. (For example mine currently shows Drowzee #96, Weedle #13, Ratata #19, Pidgey #16 etc.)
It also seems to update more frequently and accurately, every 15 seconds. Previously with the nearby system I would have to force close the app and reopen it to load a new nearby list (Personally I don't think it was properly removing pokemon from the list if they despawned). The new sightings system removes pokemon that are no longer currently in the area. This combined with the fact that there are no more duplicate listings, means the tab is less cluttered and more reliably showing what is actually around you.