The textbook definition of short-term is less than one year. Long-term is generally considered anything longer than that.
The short-term lending that most consumers might be familiar with would include pay-day and title loans. It could also include lay-away programs or a few months of installments on a purchase. There are also hard-money lenders who offer larger short-term loans analogous to a mortgage but with much shorter duration.
In most cases short-term borrowing is much costlier than long-term borrowing, which is why more people are familiar with the long-term lending options that are widely available.