Amtrak and NJ Transit are not the same route. NJ Transit pass through Secaucus, NJ also known as Secaucus Junction. Amtrak trains are a few minutes quicker and are on separate trackage. There is a map which shows the tracks side by side and I will link to it if I can find it again. Path is a different trackage altogether although there are connections at certain stations to connect between the different lines.
Penn station does share tracks inside Penn Station between NJ Transit and Amtrak on certain trains at times but I do not specifically know which lines. The Amtrak train is more direct and saves a few minutes of time. Amtrak owns their own more direct track to leave Penn Station for the Northeastern Regional and Keystone trains which have some which go to Newark Airport. All NJ Transit trains heading towards Newark Airport pass by Secaucus, NJ which is a slightly longer route. Amtrak does not own trackage in Secaucus, NJ nor share trackage with NJ Transit there. Amtrak is longer haul interstate routes so it goes from Penn Station to Newark Penn Station as its first stop south after Penn Station. NJ Transit actually connects inside NYC but all stops outside are just in NJ. PATH has multiple stations in NYC and NJ.
Found the map.
https://nycmap360.com/nyc-airports-map. Amtrak and NJ Transit have different tunnels leaving Penn station.
From first glance the Path route from 33 street in NYC has a longer route, added stops and curves which will slow down the speed vs Amtrak which is the quickest route. It does serve added places, and has a cheaper cost however and a different schedule of service. It can be quicker on some routes perhaps if you are closer by the other PATH stations. I am comparing it to the 33 street station as opposed to Penn Station. Since the PATH was already built, it made sense to have an added connection to Newark Airport. Amtrak and NI Transit can modernize their systems to run faster and more trains to Newark Airport perhaps if such was warranted but having three separate routes is nice. JFK Airtrain has a linkage to the NYC Subway and LIRR and if the LGA project goes through, will also have a link to NYC Subway and LIRR. Newark Airport will have PATH, Amtrak and NJ Transit,