Recession shapes are put to use by economists to explain different kinds of recessions. There is no particular academic theory or differentiation system for recession shapes; just the terms are used as an informal shortcut to give the property of recessions and their recoveries.
The shapes and terms most generally used are L-shaped, V-shaped, U-shaped, W-shaped, shaped recessions. There are many other shapes a recession and recovery chart would be able to take. Each shape represents the generic shape of the chart of the financial metrics that measure the strength of the economy.
The 1973-75 recession can be considered to be U-shaped because of the nearly two year time-period of zero or slow growth before recovering gradually.