“A symposium was originally ‘a Greek drinking-party that followed the evening meal’. It is from Greek ‘sym’, together, and ‘posis’, a drinking. This is the origin of the word. Now ‘symposium’ has come to mean a meeting where specialists present papers and exchange ideas. A symposiast is one who participates in a symposium. The plural of ‘symposium’ is ‘symposia’. 

‘Seminar’ means a class of advanced students who meet for some special subject under the guidance of a teacher. Such seminars take place in universities. It also means ‘a conference of specialists’ where ideas are exchanged. Seminar is from Latin word ‘seminarium’, which means a seed plot, nursery. In Latin ‘semen’ means ‘seed’. Now a seminar is a place of education, a school, a college or the like for the training of those selected for a particular profession.

Seminars are expected to be more academic than symposia but these days there is not much difference between the two. In both there are discussions and their level is not different.