We present a synthesis of fast radio burst (FRB) morphology (the change in flux as a function of time and frequency) as detected in the 400-800 MHz octave by the FRB project on the Canadian Hydrogen Intensity Mapping Experiment (CHIME/FRB), using events from the first CHIME/FRB catalog. The catalog consists of 62 bursts from 18 repeating sources, plus 474 one-off FRBs, detected between 2018 July 25 and 2019 July 2. We identify four observed archetypes of burst morphology ("simple broadband," "simple narrowband," "temporally complex," and "downward drifting") and describe relevant instrumental biases that are essential for interpreting the observed morphologies. Using the catalog properties of the FRBs, we confirm that bursts from repeating sources, on average, have larger widths, and we show, for the first time, that bursts from repeating sources, on average, are narrower in bandwidth. This difference could be due to beaming or propagation effects, or it could be intrinsic to the populations. We discuss potential implications of these morphological differences for using FRBs as astrophysical tools.