Wearables such as smartwatches provide opportunity for large-scale cardiovascular health monitoring. Wearables often use photoplethysmography (PPG), an optical sensing technique, to measure the arterial pulse wave and derive insights into cardiovascular physiology. Whilst there has been much research into the shape and physiological determinants of the finger-PPG pulse wave, much less is known about the wrist-PPG pulse wave. The aim of this study was to describe the morphology of wrist-PPG pulse waves and compare them with finger-PPG pulse waves. We analyzed wrist-PPG recordings from 686 adults in the Aurora-BP dataset. Visual inspection of pulse wave shapes revealed five classes of PPG pulse waves, three of which are similar to those seen in finger-PPG pulse waves, and two of which were different. An algorithm was developed to automatically classify wrist-PPG pulse waves, and revealed variability in pulse wave shape within and between subjects. A multivariable regression analysis of associations between subject metadata and two features of pulse wave shape indicated that wrist-PPG pulse wave shape is associated with heart rate, body size (BMI and height) and blood pressure. No significant associations with age were observed, in contrast to previous findings on finger-PPG pulse waves. The differences observed between wrist- and finger-PPG pulse wave shapes indicate a need for greater understanding of the physiological origins of the wrist-PPG pulse wave, and adaptation of algorithms specifically for wrist-PPG analysis.