Students studying at private universities in Singapore, who want to stay back and work after completing their degrees usually receive a visa extension of 1–3 months (depends on each institution). Once they get employed, an S pass is issued to them by the ICA.
On the other hand, government institutions, polytechnics and some foreign leading campuses of overseas universities usually issue Long Term Visit Pass (LTVP) which is valid for 1 year, to students who want to stay back post their studies to search for jobs in Singapore.