Is there a difference between a symposium paper and a conference paper My university requires for PhD candidates to publish 1 journal paper + 2 conference papers in order to be able to proceed to the viva. 

Recently, I submitted a paper to a symposium that has a proceeding with an ISBN. The proceeding, however, will not be published online (only a hard copy, but I found the citations of previous conference in google scholar). The paper is accepted and today is the deadline to pay the registration fees. Both the university direction and my supervisor did not respond to my emails, so I have to make the decision on my own.

My question is: can we call a symposium paper a conference paper? And is there any difference in terms of quality?

My domain is Project Management.
AFAIK, a symposium is essentially the same as a conference.  I think it tends to suggest a somewhat smaller size, historically, but definitely bigger and more competitive than a workshop.  For instance the ACM Symposium on Operating Systems Principles is one of the most competitive conferences in the computer systems field, and gets maybe 500-600 attendees these days.  Some "conferences" get many thousands, though some get only 50-100 too.  

Now, perhaps in other fields than computer science, there is a completely different definition, but if you have to pull the trigger, you should assume it is a conference and not a workshop.  

Besides, you submitted the paper and they accepted it.  It would be really poor form to pull out right now, even if somehow it didn't count toward your graduation.  Didn't your advisor know you were submitting it, and think it was a good idea?