When I went to school in the US (a while ago now), we just paid the loan off in installments just like any loan. Most of the loans were from private lenders. Recently, early in the Obama administration, the federal government basically took over the student loan industry.
This was a perfectly workable system for a very long time, but a lot of rot and corruption came into the education system over the years, and recent attempts to fix it just makes it worse. They have been playing the game of raising their tuition at a much higher rate than inflation for at least two decades now, but they always cry poverty, so the states and federal governments step in with even more money.
The students are the genuine victims, but bailing them out also bails out the people that caused this mess. The education industry is trying to keep the bailouts coming, but without admitting they are the cause of the problems or undertaking any real reform.
You left out the part about student loans have special interest rates and delayed payment schedules and they were subsidized by the federal government.