This got me thinking, so I looked it up in my Cdn Oxford. All I found for "philharmonic" was:

1. fond of music
2. used characteristically in the names of orchestras, choirs etc.

Then for "symphony orchestra" I found:

a large orchestra suitable for playing symphonies etc.

So many it does have to do with the composition? maybe you need to have a certain number and variety of instruments to be a "symphony orchestra"? Just a thought....