Stellar variability is driven by various processes occurring at the stellar surface and in the stellar interior, such as due to stellar eclipses, flares, tidal interactions, pulsations, spots, and rotation. We use unsupervised machine learning on photometric light curves observed by the Transiting Exoplanet Survey Satellite (TESS) to conduct a census of different types of stellar variability. Towards this purpose, we use a one-dimensional convolutional autoencoder and feature engineering, which yields compressed, low-dimensional representations of the data. We use the learned representations to perform large-scale classification and novelty detection using TESS light curves. We validate our pipeline using the General Catalogue of Variable Stars, which contains 54,821 stars primarily in the Milky Way galaxy. Using only single and broadband photometric data from two sectors of TESS observations, ~50% of our stellar variability class predictions agree with those in the General Catalog of Variable Stars. The indiscriminate survey produced by TESS offers a unique opportunity to investigate the relationships between light curve features and underlying stellar characteristics such as type, age, metallicity, and mass. Our homogeneous census of stellar variability will lead to a better understanding of the underlying demographics.