Both terms originate in the Greek language - philharmonic means "loving harmony" and symphonic means "sounding together, and in the modern orchestra, the two are interchangable. There is no difference in instrumentation between the two - the only difference occurs in repertoire - the Symphony Orchestra, as the name suggests, veers towards a programme of symphonic music, but a Philharmonic Orchestra can play a symphony as well, so the simple answer is - there is no difference.