In a closed system the breathers are solid in appearance and have hoses attached to them that run to the air cleaner/manifold to make sure the fumes are burned during combustion. Open breathers usually have holes on the bottom edges and you can see the packing in them....they simply let the fumes/smoke enter into the engine compartment.
It really only matters what you have when the smog laws in your state require a closed system for your year vehicle if so equipped from the factory....this is usaully only in CA on cars from the 60s IIRC.
There are several other solutions or rather variations on the open/closed.
One can also draw a vacuum on there crankcase by using a pump or the method I use. I have tubes welded into the collectors of my headers. braided lines rune from the tube, through a check valve (anti-backfire) and into the breathers. The exhaust "sucks" on the crankcase in proportion to RPM.