Context. Light-curve variability is well-suited to characterising objects in surveys with high cadence and a long baseline. This is especially relevant in view of the large datasets to be produced by the Vera C. Rubin Observatory Legacy Survey of Space and Time (LSST). Aims. We aim to determine variability parameters for objects in the Palomar Transient Factory (PTF) and explore differences between quasars (QSOs), stars, and galaxies. We relate variability and colour information in preparation for future surveys. Methods. We fit joint likelihoods to structure functions (SFs) of 71 million PTF light curves with a Markov chain Monte Carlo method. For each object, we assume a power-law SF and extract two parameters: the amplitude on timescales of one year, A, and a power-law index, γ. With these parameters and colours in the optical (Pan-STARRS1) and mid-infrared (WISE), we identify regions of parameter space dominated by different types of spectroscopically confirmed objects from SDSS. Candidate QSOs, stars, and galaxies are selected to show their parameter distributions. Results. QSOs show high-amplitude variations in the R band, and the highest γ values. Galaxies have a broader range of amplitudes and their variability shows relatively little dependency on timescale. With variability and colours, we achieve a photometric selection purity of 99.3% for QSOs. Even though hard cuts in monochromatic variability alone are not as effective as seven-band magnitude cuts, variability is useful in characterising object subclasses. Through variability, we also find QSOs that were erroneously classified as stars in the SDSS. We discuss perspectives and computational solutions in view of the upcoming LSST.