Phantom 3 Standard specs say "Software altitude limit: 120 m above takeoff point".The same line in Phantom 3 Advanced specs says: "Default altitude limit: 120 m above takeoff point".
Default limit means you can change the limit to higher values (up to 500m). It's not obvious from description that I can change Standard model "software limit".

Can I change Standard max height as well or is it forever limited to 120m?

  You are able to change it to my understanding.

yes  can change it , but remember that there is some helicopters or birds   just be careful
if you change it to 500 meters let me know what range you get ,  with the standard i only get 100 to 200 meters of altitude before lose RC signal

Ive gotten 330 meters altitude from my standard before a RTH. ive added a wifi signal reflector to my controller but havent tested since but it did seem to improve signal strength.

I have had a maximum 1,556 feet with my P3S still getting the advance though iv heard lightbridge is much better

You can set the maximum altitude in "MC Settings" .