Philadelphia Orchestra 2
The Philadelphia Orchestra is a professional full-time orchestra. It is considered one of the elite orchestras in the world. By that definition, it is a philharmonic orchestra, though "philharmonic" is usually just part of a title. I.E. New York
Philharmonic, Los Angeles
Philharmonic, Boston
Philharmonic (which is actually a semi-professional orchestra) There really is no difference between a Philharmonic, or a Symphony Orchestra, or just an Orchestra and usually very little can be inferred from a title of one.
The correct name for the organization is The Philadelphia Orchestra always with a capital T in The.