What is the difference between the long run and short run Phillips curves?

The Phillips Curve describes the relation between output and inflation. It proposes that there is a positive relation between these two variables, so that decreasing inflation comes at the cost of lower output. The short-run PC is drawn for a given value of inflation expectations, whilst the long-run PC is drawn for when inflation and inflation expectations are equal. 

Different schools of thought have proposed different slopes for the long and short run curves. For example, in the New Keynesian school of thought, the LRPC has a positive slope, implying there is a trade off between inflation and output even in the long-run. However, in the Classical school of thought, there is no such trade off in the long-run. 

The trade-off between inflation and output recieves robust empirical support. For example, Ball (1994) measured the costs of disinflation (a decrease in inflation, which is different from deflation when inflation is negative) across 19 OECD countries, and found that there was a significant positive relationship between disinflation and output loss.