Transiting Exoplanet Survey Satellite (TESS) photometry of the polars AM Herculis (AM Her) and AR Ursae Majoris (AR UMa) is presented, along with high-speed photometry. AM Her shows a variety of high states with frequent transitions between them. TESS photometry of AR UMa in the low state reveals no evidence of accretion, while the McDonald 2.1 m telescope caught AR UMa in its high accretion state. Roche-lobe overflow is shut off during low states of AR UMa, while accretion often still takes place during low states of AM Her. We derive inclinations of 50° and 70° for AM Her and AR UMa respectively. To model the high-state light curves of AM Her, we employ a self-organized map light-curve classification scheme to establish common accretion configurations. The cyclotron radiation properties then allow the production of emission region maps on the surface of the white dwarf. The accretion geometry of AM Her is most consistent with a multipolar field structure. The high-state photometry of AR UMa has stochastic accretion flaring, which we attribute to magnetically buffeted mass transfer through the inner Lagrangian point L1. To consider this possibility, we examine the magnetism of both stars and argue that the local magnetic field near L1 can initiate short-lived accretion events and affect transitions between high and low accretion states in both AM Her and AR UMa. In particular, AR UMa has the low state as its default, while AM Her and most other active polars are in the high state by default.