Whether you call the Supreme Lord Ram as Sriram or Siyaram
or Sitaram it means one and the same as referring to the Lord of
Sita. Sri refers to Lakshmi and Sita is the clear manifestation
of Lakshmi only.
When the Lord takes the form of Rama, Lakshmi appears in
the form of Sita only. This is authenticated by the reference
“राघवत्वेऽभवत् सीता रुक्मिणी कृष्णजन्मनि"from Sri Vishnu Purana.
Though only Sitaram or Siyaram is intended, it is the
accepted practice to write “Sriramajayam”. Thus,there is
absolutely no difference between Jai Sriram
and Jai Siyaram.
जय जय श्रीराधे