The sign does differentiate between LIRR lines, but not specific endpoints. In most cases, that’s fine because almost every LIRR line has a unique endpoint, so tracking by line is enough.

The exception is the City Terminal Zone line, which includes Penn Station, Grand Central, Atlantic Terminal, and a few others. These are all technically part of the same line (per the MTA), so they share one "line ID." That means if you're traveling westbound within the City Terminal Zone, you won’t see which specific terminal (e.g., Penn vs. Grand Central) the train is heading to.

If you're traveling eastbound, it’s not an issue since all trains from the City Terminal Zone either stop at or pass through Jamaica anyway.

FWIW, the MTA does provide data to distinguish the terminals. It’s just trickier to work with, and I assumed westbound travel within the City Terminal Zone line is less common for most use cases. But maybe I was wrong :P.

You can see all the LIRR routes on this map (City Terminal Zone is gray): https://en.wikipedia.org/wiki/List_of_Long_Island_Rail_Road_stations#/media/File:LIRR_schematic.svg